Caractère de Chern bivariant. (Bivariant Chern character) (Q913940)

With \textit{J. D. S. Jones}, the author has introduced bivariant cyclic cohomology groups \(HC^*(A,B)\) for pairs of algebras A and B [ibid. 3, No.4, 339-365 (1989)]. In this paper he develops the theory further. He then introduces a Grothendieck group K(A,B) of A-B-bimodules and shows that there is a multiplicative Chern character ch: K(A,B)\(\to HC^ 0(A,B)\). He also constructs a Chern character for quasi-homomorphisms with homologically unital codomains. This Chern character is homotopy invariant, provided that its values are regarded as lying in periodic bivariant cyclic cohomology groups.