Configuration spaces of orbits and their $S_n$-equivariant $E$-polynomials

In this paper, we introduce the configuration space of orbits, a generalization of the configuration space of points but for algebraic varieties that are acted by an algebraic reductive group. We develop a novel method for computing the $S_n$-equivariant $E$-polynomial of an algebraic variety, and we apply it to this new kind of varieties.
Comment: 22 pages. Comments are welcome