Generating Functions of Orbifold Chern Classes I : Symmetric Products

For a possibly singular complex variety $X$, generating functions of total “orbifold Chern homology classes” of symmetric products $S^{n}X$ are given. Those are very natural “Chern class versions” (in the sense of Schwartz-MacPherson) of known generating function formulae of (generalized) orbifold Euler characteristics of $S^{n}X$. In fact more generally we introduce the “class version” of the Dey-Wohlfahrt formula in classical group theory.