2. This Regulation applies to the processing of personal data of data subjects who are in the Union by a controller or processor not established in the Union, where the processing activities are related to:
(a) the offering of goods or services, irrespective of whether a payment of the data subject is required, to such data subjects in the Union; or
(b) the monitoring of their behaviour as far as their behaviour takes place within the Union.
2. The obligation laid down in paragraph 1 of this Article shall not apply to:
(a) processing which is occasional, does not include, on a large scale, processing of special categories of data as referred to in Article 9(1) or processing of personal data relating to criminal convictions and offences referred to in Article 10, and is unlikely to result in a risk to the rights and freedoms of natural persons, taking into account the nature, context, scope and purposes of the processing; or
1. Processing of personal data revealing racial or ethnic origin, political opinions, religious or philosophical beliefs, or trade union membership, and the processing of genetic data, biometric data for the purpose of uniquely identifying a natural person, data concerning health or data concerning a natural person’s sex life or sexual orientation shall be prohibited.
Article 10 GDPR. Processing of personal data relating to criminal convictions and offences
Processing of personal data relating to criminal convictions and offences or related security measures based on Article 6(1) shall be carried out only under the control of official authority or when the processing is authorised by Union or Member State law providing for appropriate safeguards for the rights and freedoms of data subjects. Any comprehensive register of criminal convictions shall be kept only under the control of official authority.
The GDPR does not define what constitutes a ‘public authority or body’. The WP29 considers that such a notion is to be determined under national law. Accordingly, public authorities and bodies include national, regional and local authorities, but the concept, under the applicable national laws, typically also includes a range of other bodies governed by public law . In such cases, the designation of a DPO is mandatory.
 See, e.g. the definition of ‘public sector body’ and ‘body governed by public law’ in Article 2(1) and (2) of Directive 2003/98/EC of the European Parliament and of the Council of 17 November 2003 on the re-use of public-sector information (OJ L 345, 31.12.2003, p. 90).
A public task may be carried out, and public authority may be exercised  not only by public authorities or bodies but also by other natural or legal persons governed by public or private law, in sectors such as, according to national regulation of each Member State, public transport services, water and energy supply, road infrastructure, public service broadcasting, public housing or disciplinary bodies for regulated professions.
 Article 6(1)(e).
3. The representative shall be established in one of the Member States where the data subjects, whose personal data are processed in relation to the offering of goods or services to them, or whose behaviour is monitored, are.
Offering of goods or services, irrespective of whether a payment of the data subject is required, to data subjects in the Union
The first activity triggering the application of Article 3(2) is the “offering of goods or services”, a concept which has been further addressed by EU law and case law, which should be taken into account when applying the targeting criterion. The offering of services also includes the offering of information society services, defined in point (b) of Article 1(1) of Directive (EU) 2015/1535  as “any Information Society service, that is to say, any service normally provided for remuneration, at a distance, by electronic means and at the individual request of a recipient of services”.
 Directive (EU) 2015/1535 of the European Parliament and of the Council of 9 September 2015 laying down a procedure for the provision of information in the field of technical regulations and of rules on Information Society services.
Another key element to be assessed in determining whether the Article 3(2)(a) targeting criterion can be met is whether the offer of goods or services is directed at a person in the Union, or in other words, whether the conduct on the part of the controller, which determines the means and purposes of processing, demonstrates its intention to offer goods or a services to a data subject located in the Union. Recital 23 of the GDPR indeed clarifies that “in order to determine whether such a controller or processor is offering goods or services to data subjects who are in the Union, it should be ascertained whether it is apparent that the controller or processor envisages offering services to data subjects in one or more Member States in the Union.”
4. The representative shall be mandated by the controller or processor to be addressed in addition to or instead of the controller or the processor by, in particular, supervisory authorities and data subjects, on all issues related to processing, for the purposes of ensuring compliance with this Regulation.
5. The designation of a representative by the controller or processor shall be without prejudice to legal actions which could be initiated against the controller or the processor themselves.
General Data Protection Regulation (EU GDPR)
The latest consolidated version of the Regulation with corrections by Corrigendum, OJ L 127, 23.5.2018, p. 2 ((EU) 2016/679). Source: EUR-lex.
(80) Where a controller or a processor not established in the Union is processing personal data of data subjects who are in the Union whose processing activities are related to the offering of goods or services, irrespective of whether a payment of the data subject is required, to such data subjects in the Union, or to the monitoring of their behaviour as far as their behaviour takes place within the Union, the controller or the processor should designate a representative, unless the processing is occasional, does not include processing, on a large scale, of special categories of personal data or the processing of personal data relating to criminal convictions and offences, and is unlikely to result in a risk to the rights and freedoms of natural persons, taking into account the nature, context, scope and purposes of the processing or if the controller is a public authority or body. The representative should act on behalf of the controller or the processor and may be addressed by any supervisory authority. The representative should be explicitly designated by a written mandate of the controller or of the processor to act on its behalf with regard to its obligations under this Regulation. The designation of such a representative does not affect the responsibility or liability of the controller or of the processor under this Regulation. Such a representative should perform its tasks according to the mandate received from the controller or processor, including cooperating with the competent supervisory authorities with regard to any action taken to ensure compliance with this Regulation. The designated representative should be subject to enforcement proceedings in the event of non-compliance by the controller or processor.
ISO/IEC 27701, adopted in 2019, added a requirement additional to ISO/IEC 27002, section 6.1.1.
Here is the relevant paragraph to article 27 GDPR:
184.108.40.206 Information security roles and responsibilities
The organization should designate a point of contact for use by the customer regarding the processing of PII. When the organization is a PII controller, designate a point of contact for PII principals regarding the processing of their PII (see 7.3.2).
The organization should appoint one or more persons responsible for developing, implementing, maintaining and monitoring an organization-wide governance and privacy program, to ensure compliance with all applicable laws and regulations regarding the processing of PII.
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