KK-theory of C*-categories and the analytic assembly map

Abstract

We define KK-theory spectra associated to C*-categories and look at certain instances of the Kasparov product at this level. This machinery is used to give a description of the analytic assembly map as a natural map of spectra.Comment: This is an updated version of an existing article. In this new version the machinery developed works in greater generality than the old versio