  Motivic integration and MacPherson's transformation are combined in this
paper to construct a theory of "stringy" Chern classes for singular varieties.
These classes enjoy strong birational invariance properties, and their
definition encodes data coming from resolution of singularities. The
singularities allowed in the theory are those typical of the minimal model
program; examples are given by quotients of manifolds by finite groups. For the
latter an explicit formula is proven, assuming that the canonical line bundle
of the manifold descends to the quotient. This gives an expression of the
stringy Chern class of the quotient in terms of Chern-Schwartz-MacPherson
classes of the fixed-point set data.
