Equivariant bivariant cyclic theory and equivariant chern-connes character

Abstract

We construct an equivariant bivariant cyclic theory, as a combination of equivariant cyclic andnoncomm utative de Rham theories for unital G-Banach algebras, where G is a compact Lie group. By incorporating the JLO formula andthe superconnection formalism of Quillen, an equivariant bivariant Chern Connes character of Kasparov’s G-bimodule is defined, with values in the bivariant cyclic theory.