European Union officials are expected to issue a record fine of at least 1.1 billion euros, or $1.2 billion, against Google as soon as Tuesday for breaking the region’s tough competition rules.

Yet the hefty penalty and its timing, which were confirmed by two people with knowledge of the matter who spoke on the condition of anonymity, are likely to be quickly overshadowed by a more complex problem: How should Google comply with the decision to rein in its power?

That dilemma will now take center stage as the tech giant fights doggedly to protect its crown jewel — its closely guarded search algorithm — from the prying eyes of regulators and, possibly, its competitors.

Potentially heavy-handed intervention may raise the hackles of Google and other companies in the American tech world, which could claim that, once again, Europe is unfairly targeting companies from the United States. The region’s officials deny such accusations.