ИСТИНА

For a topological space with a finite group action, higher order Euler characteristics are generalizations of the orbifold Euler characteristic introduced by physicists. The generating series of thehigher order Euler characteristics of a fixed order of the Cartesian products of the manifold with the wreath product actions on them were computed by H. Tamanoi. There were constructed two types of generalizations of these notions. First, one constructed (for an action on a complex quasi-projective manifold) motivic versions of the higher order Euler characteristics with values in the Grothendieck ring of complex quasi-projective varieties extended by the rational powers of the class of the affine line. Second, one constructed analogues of higher order Euler characteristics for actions of compact Lie groups. There were given formulae for the generating series of these generalized Euler characteristics for the wreath product actions. For the motivic version the formulae are given in terms of the power structure over the (extended) Grothendieck ring of complex quasi-projective varieties defined earlier. The talk is based on joint works with I. Luengo and A. Melle-Hernandez.