[samus]

If the companies don't have assets in the EU that can be affected by EU prosecution, then the GDPR is not enforceable. It might be possible to prosecute and trial management, but again this has only consequences if they enter EU jurisdiction or if they are extradited. Such issues and questions always arise with laws whose reach is extraterritorial. Keep in mind that the US has a fair number of these laws as well.

[fnord77]

deny entry or arrest executives of the company if they try to enter the EU. Surely some of these people travel...

[samus]

Yes, that would work. It's what the US does after all. I'm not optimistic though thah the EU is capable and mature enough to handle the ensuing diplomatic heat. At least not yet.