Entropy of automorphisms arising from dynamical systems through discrete groups with amenable actions

Let G subset of Aut(A) be a discrete group which is exact, that is, admits an amenable action on some compact space. Then the entropy of an automorphism of the algebra A does not change by the canonical extension to the crossed product A x G. This is shown for the topological entropy of an exact C*-algebra A and for the dynamical entropy of an AFD von Neumann algebra A. These have applications to the case of transformations on Lebesgue spaces. (C) 2004 Elsevier Inc. All rights reserved.