Finite group actions on dg categories and Hochschild homology

We prove a decomposition of the Hochschild homology groups of the equivariant dg category CG associated to a small dg category C with direct sums on which a finite group G acts. When the ground field is C this decomposition is related to a categorical action of Rep (G) on CG and the resulting action of the representation ring RC (G) on HH_ (CG).