  We shall present a simplified version of a construction due to Denis Perrot
that recovers the Todd class of the complexified tangent bundle from a JLO-type
cyclic cocycle. The construction takes place within an algebraic framework,
rather than the customary functional-analytic framework for the JLO theory. The
series expansion for the exponential function is used in place of the heat
kernel from the functional-analytic theory; the Dirac operator chosen is far
from elliptic; and a remarkable new trace discovered by Perrot replaces the
operator trace. In its full form Perrot's theory constitutes a wholly new
approach to index theory. The account presented here covers most but not all of
this approach.
