(22) Any processing of personal data in the context of the activities of an establishment of a controller or a processor in the Union should be carried out in accordance with this Regulation, regardless of whether the processing itself takes place within the Union.
Establishment implies the effective and real exercise of activity through stable arrangements.
The legal form of such arrangements, whether through a branch or a subsidiary with a legal personality, is not the determining factor in that respect.
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.