The Chern character of semifinite spectral triples

In previous work we generalised both the odd and even local index formula ofConnes and Moscovici to the case of spectral triples for a *-subalgebra \A of ageneral semifinite von Neumann algebra. Our proofs are novel even in thesetting of the original theorem and rely on the introduction of a functionvalued cocycle (called the resolvent cocycle) which is `almost' a (b,B)-cocyclein the cyclic cohomology of \A. In this paper we show that this resolventcocycle `almost' represents the Chern character, and assuming analyticcontinuation properties for zeta functions, we show that the associated residuecocycle, which appears in our statement of the local index theorem doesrepresent the Chern character.