AbstractLet Λ be a finite-dimensional algebra andGbe a finite group whose elements act on Λ as algebra automorphisms. Assume that Λ has a complete setEof primitive orthogonal idempotents, closed under the action of a Sylowp-subgroupS≤G. If the action ofSonEis free, we show that the skew group algebra ΛGand Λ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra ΛSis a direct summand of the ΛS-bimodule Λ. Using a homological characterization of piecewise hereditary algebras proved by Happel and Zacharia, we deduce a criterion for ΛGto be piecewise hereditary.