Skew group algebras of piecewise hereditary algebras are piecewise hereditary

We show that the main results of Happel–Rickard–Schofield (1988) and Happel–Reiten–Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if GG is a finite group acting on a piecewise hereditary algebra AA over an algebraically closed field whose characteristic does not divide the order of GG, then the resulting skew group algebra A[G]A[G] is also piecewise hereditary.