  Let a finite group G act on a differential graded algebra A. This article
presents necessary conditions and sufficient conditions for the skew group
algebra A*G to be Calabi-Yau. In particular, when A is the Ginzburg dg algebra
of a quiver with an invariant potential, then A*G is Calabi-Yau and Morita
equivalent to a Ginzburg dg algebra. Some applications of these results are
derived to compare the generalised cluster categories of A and A*G when they
are defined and to compare the higher Auslander-Reiten theories of A and A*G
when A is a finite dimensional algebra.
