The obstruction to excision in K-theory and in cyclic homology

Let f:A→B be a ring homomorphism of not necessarily unital rings and an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K_*(A:I)→K_*(B:f(I)) to be an isomorphism; it is measured by the birelative groups K_*(A,B:I). Similarly the groups HN_*(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism