Grumbler, ACTORS act, not criminals. I would just say: "INfamous American robbers DURING the Great Depression." When you're famous for something bad, you're INFAMOUS [и́нфъмъс].

noted and corrected - транскрипция есть в словаре
Не очень понятно насчет act. Пороюсь поглубже, когда будет время.

I meant that when ACT is used as in your sentence without an adverb describing someone’s behavior, it usually relates to acting in film or on stage: Brad Pitt acted in three movies before he became famous.