The GDPR relies on international treaties to make the ___location of the business irrelevant. Any company processing data of EU citizens must comply IIRC.
Do you have any pointers to where I can find info on that? It's clear that the GDPR itself establishes jurisdiction for EU courts over GDPR worldwide - it's very explicit about that.
But I can't find anything about how they'd make it enforceable in other jurisdictions (as opposed to enforcing the judgements by e.g. fining EU subsidiaries and the like).
Article 50 does say the Commission should take "appropriate steps" to ensure international "cooperation mechanisms", and its clear under e.g article 44 onwards that carrying out a transfer to a jurisdiction where the data would be subject to inadequate controls would be a violation of the directive, so you may very well be right.