  Given a smooth action of a Lie group on a manifold, we give two constructions
of the Chern character of an equivariant vector bundle in the cyclic cohomology
of the crossed product algebra. The first construction associates a cycle to
the vector bundle whose structure maps are closely related to Getzler's model
for equivariant cohomology. The second construction uses a direct map between
this model and the (periodic) cyclic cohomology localized at the unit element.
Finally, it is shown that the two constructions are equivalent when the action
is proper.
