Bivariant Chern character and the longitudinal index theory
Abstract
In this paper we consider a family of Dirac-type operators on fibration P B equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map in the cyclic cohomology. A particular case of this result is Connes' index theorem for etale groupoids in the case of fibrations.
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