On deformations of crossed products

Let A (*) Gamma be a crossed product algebra, where A is semisimple, finitely generated over its center and Gamma is a finite group. We give a necessary and sufficient condition in terms of the outer action of Gamma on A for the existence of a multi-parametric semisimple deformation of the form A((t(1),..., t(n))) (*) Gamma (with the induced outer action). The main tool in the proof is the solution of the so-called twisting problem. We also give an example which shows that the condition is not sufficient if one drops the condition on the finite generation of A over its center. (c) 2006 Elsevier B.V. All rights reserved.