%0 Journal Article %A Gusein Zade, S.M. %A Luengo Velasco, Ignacio %A Melle Hernández, Alejandro %T Higher order generalized Euler characteristics and generating series %D 2015 %@ 0393-0440 %U https://hdl.handle.net/20.500.14352/24120 %X For a complex quasi-projective manifold with a finite group action, we define higher order generalized 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. 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. %~