ИСТИНА

For a ”good enough” topological space with a finite group action, higher order orbifold Euler characteristics are generalizations of the orbifold Euler characteristic introduced by physicists. One has computed the generating series of the higher order Euler character- istics of a fixed order of the Cartesian products of the manifold with the wreath product actions on them (getting formulae of MacDonald type). We discuss some generalizations of these notions. They include their motivic versions (with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the class of the affine line) and their versions for compact Lie group actions. We give formulae for the generating series of these generalized Euler characteristics for the wreath product actions. The talk is based on joint works with I. Luengo and A. Melle-Hernndez.