On the irreducible representations of generalized quantum doubles

A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld doubles is obtained. It is shown that the Grothendieck ring of these generalized quantum doubles have a structure similar to the rings that arise from Green functors. In order to do this we give a formula for the tensor product of any two such irreducible representations.