Multiplicative property of localized Chern characters for 2-periodic complexes

Abstract

We prove the multiplicative property of localized Chern characters. As a direct consequence, a localized Chern character gives rise to a ring homomorphism from the K-group of periodic complexes to the bivariant Chow cohomology group. As an application, we prove the functoriality of Kiem-Li's cosection-localized intersection homomorphisms.