Crossed Products byC0(X)-Actions

Abstract

Suppose thatGhas a representation groupH, thatGabG/[G,G]is compactly generated, and thatAis aC*-algebra for which the complete regularization of Prim(A) is a locally compact Hausdorff spaceX. In a previous article, we showed that there is a bijectionα(Zα,fα) between the collection of exterior equivalence classes of locally inner actionsα:G→Aut(A), and the collection of principalGab-bundlesZαtogether with continuous functionsfα:X→H2(G,T). In this paper, we compute the crossed productsA⋊αGin terms of the dataZα,fα, andC*(H). © 1998 Academic Press.