TITLE: Reference for a Maschke lemma for crossed products
QUESTION [6 upvotes]: Can someone provide a reference for the following Maschke lemma:
If $C$ is a semisimple algebra over a field of characteristic zero and $G$ is a finite group
acting on $C$ by automorphisms, then $C \rtimes G$ is semisimple.

REPLY [2 votes]: This is also stated in the generality asked for as Theorem 1.3 (c) in [Reiten, Riedtmann: Skew group algebras in the representation theory of Artin algebras, Journal of Algebra 92, 1985].