Bundles of C*-categories, II: C*-dynamical systems and Dixmier-Douady invariants

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As an application, the duality breaking for group bundles vs. tensor C*-categories with non-simple unit is discussed in the setting of Nistor-Troitsky gauge-equivariant K-theory: there is a map assigning a nonabelian gerbe to a tensor category, and "triviality" of the gerbe is equivalent to the existence of a dual group bundle. At the C*-algebraic level, this corresponds to studying C*-algebra bundles with fibre a fixed-point algebra of the Cuntz algebra and in this case our invariant describes the obstruction to finding an embedding into the Cuntz-Pimsner algebra of a vector bundle.Comment: 27 pages; contains a revised version of the second part of math/0510594v1. A new section on gauge actions on C*-bundles has been added, and nonabelian gerbes have been considered as invariants associated with tensor C*-categorie

The C*-algebra of a vector bundle and fields of Cuntz algebras

We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.Comment: 37 page