The Generalized Chern Character and Lefschetz Numbers in W*-Modules

We define N-theory as being an analogue of K-theory on the category of von Neumann algebras such that K0(A)⊂N0(A) for any von Neumann algebra A. Moreover, it turns out to be possible to construct the extension of the Chern character to some homomorphism from N0(A) to an even Banach cyclic homology of A. Also, we define generalized Lefschetz numbers for an arbitrary unitary endomorphism U of an A-elliptic complex. We study them in the situation when U is an element of a representation of some compact Lie group.