Equivariant Chern classes of singular algebraic varieties with group actions

We define equivariant Chern-Schwartz-MacPherson classes of a possibly singular algebraic G-variety over the base field C, or more generally over a field of characteristic 0. In fact, we construct a natural transformation C-*(G) from the G-equivariant constructible function functor F-G to the G-equivariant homology functor H-*(G) or A(*)(G) (in the sense of Totaro-Edidin-Graham). This C-*(G) may be regarded as MacPherson's transformation for (certain) quotient stacks. The Verdier-Riemann-Roch formula takes a key role throughout.