Higher order Euler characteristics are generalizations of the so-called orbifold Euler characteristic (for a space with a finite group action) introduced by physisists. For a complex quasi-projective manifold with a finite group action, we define higher order generalized Euler characteristics (a sort of 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. We compute the generating series of generalized Euler characteristics of a fixed order of the Cartesian products of the manifold with the wreath product actions on them.
The talk is based on a joint work with I.Luengo and A.Melle-Hernandez.