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 I∇A 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). We show that these are rationally isomorphic to the corresponding birelative groups for cyclic homology up to a dimension shift. In the particular case when A and B are Q-algebras we obtain an integral isomorphism. (author)