  The Chern character of a complex vector bundle is most conveniently defined
as the exponential of a curvature of a connection. It is well known that its
cohomology class does not depend on the particular connection chosen. It has
been shown by Quillen that a connection may be perturbed by an endomorphism of
the vector bundle, such as a symbol of some elliptic differential operator.
This point of view, as we intend to show, allows one to relate Chern character
to a non-commutative sibling formulated by Connes and Moscovici. The general
setup for our problem is purely geometric. Let \sigma be the symbol of a
Dirac-type operator acting on sections of a \Z_2-graded vector bundle E. Let
\nabla be a connection on E, pulled back to T^*M. Suppose also that \nabla
respects the Z_2-grading. The object \nabla+\sigma is a superconnection on T^*M
in the sense of Quillen. We obtain a formula for the H_*(M)-valued Poincare
dual of Quillen's Chern character ch(D)=trace(exp(\nabla+\sigma)^2) in terms of
residues of \Gamma(z)trace(\nabla+\sigma)^{-2z}. We also compute two examples.
