Y-system for Z_S Orbifolds of N=4 SYM

We propose a twisted Y-system for the calculation of leading wrapping corrections to physical states of general Z_S orbifold projections of N=4 super Yang-Mills theory. Agreement with available thermodynamical Bethe Ansatz results is achieved in the non supersymmetric case. Various examples of new computations, including other supersymmetric orbifolds are illustrated.