On the motive of quotients of induced actions

Abstract: We explore computational tools that allow to compute the class on the Grothendieck ring of varieties of finite cyclic quotients in some interesting examples. As an main application, we determine the motive of low rank representation varieties associated with torus knots and general linear groups using an equivariant analogue of the strategy for special linear groups due to A.Gonz\'alez-Prieto and V.Mu~noz.