Generating series of classes of exotic un-ordered configuration spaces

A notion of exotic (ordered) configuration spaces of points on a space X was suggested by Yu. Baryshnikov. He gave equations for the (ex-ponential) generating series of the Euler characteristics of these spaces. Here we consider un-ordered analogues of these spaces. For X being a complex quasiprojective variety, we give equations for the generating series of classes of these configuration spaces in the Grothendieck ring K 0 (Var C ) of complex quasiprojective varieties. The answer is formulated in terms of the (natural) power structure over the ring K 0 (Var C ). This gives equations for the generating series of additive invariants of the configuration spaces such as the Hodge–Deligne polynomial and the Euler characteristic.