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In previous papers the authors gave formulae for generating series of classes(in the Grothendieck ring of complex quasi-projective varieties) of Hilbertschemes of zero-dimensional subschemes on smooth varieties and on orbifolds interms of certain local data and the, so called, power structure over thecorresponding ring. Here we give an analogue of these formulae for equivariant(with respect to an action of a finite group on a smooth variety) Hilbertschemes of zero-dimensional subschemes and compute some local generating seriesfor an action of the cyclic group on a smooth surface.

On generating series of classes of equivariant Hilbert schemes of fat points