Solution of the twisting problem for skew group algebras

LetK be any field of characteristicp>0 and letG be a finite group acting onK via a map τ. The skew group algebraK _τG may be nonsemisimple (precisely whenP|(H), H=Kert). In 1] necessary conditions were given for the existence of a class α∈H ²(G,K^*) which “twists” the skew group algebraK _τG into a semisimple crossed productK _τ ^αG . The “twisting problem” asks whether these conditions are sufficient. In 1] we showed that this is indeed so in many cases. In this paper we prove it in general. During the period of this research the second author was an Associate at the Center for Advanced Study, Urbana, Illinois.