Crossed Products byC0(X)-Actions

Suppose thatGhas a representation groupH, thatGab≔G/[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).