Finitistic dimensions and piecewise hereditary property of skew group algebras

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Let Λ be a finite dimensional algebra and G be a finite group whose elements act on Λ as algebra automorphisms. Under the assumption that Λ has a complete set E of primitive orthogonal idempotents, closed under the action of a Sylow p-subgroup S G. If the action of S on E is free, we show that the skew group algebra ΛG and Λ have the same finitistic dimension, and have the same strong global dimension if the fixed algebra Λˢ is 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 ΛG to be piecewise hereditary.