  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.
