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

We study the Cuntz-Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. Furthermore, we assign to bundles of Cuntz algebras carrying a global circle action a class in the representable KK-group of the zero-grade bundle. We explicitly compute such class for the Cuntz-Pimsner algebra of a vector bundle.