Representations of crossed products by coactions and principal bundles

Abstract

The main purpose of this paper is to establish a covariant representation theory for coactions of locally compact groups on C ∗ {C^{\ast }} -algebras (including a notion of exterior equivalence), to show how these results extend the usual notions for actions of groups on C ∗ {C^{\ast }} -algebras, and to apply these ideas to classes of coactions termed pointwise unitary and locally unitary to obtain a complete realization of the isomorphism theory of locally trivial principal G G -bundles in this context. We are also able to obtain all (Cartan) principal G G -bundles in this context, but their isomorphism theory remains elusive.