Quasihomomorphisms and the residue Chern character

We develop a general procedure, based on the renormalized eta-cochain, which allows to find “local” representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization we obtain a bivariant generalization of the Connes–Moscovici residue formula, and explain the link with chiral and multiplicative anomalies in quantum field theory.