  We show that the bivariant Chern character in entire cyclic cohomology
constructed in a previous paper in terms of superconnections and heat kernel
regularization, retracts on periodic cocycles under some finite summability
conditions. The trick is a bivariant generalization of the Connes-Moscovici
method for finitely summable K-cycles. This yields concrete formulas for the
Chern character of p-summable quasihomomorphisms and invertible extensions,
analogous to those of Nistor. The latter formulation is completely algebraic
and based on the universal extensions of Cuntz and Zekri naturally appearing in
the description of bivariant K-theory.
