[en] In this paper superstring solutions on twisted group manifolds are investigated, chiefly in the case of fermionizable Wess-Zumino-Witten models that yield space-time N = 1 supersymmetry. Both outer and inner automorphisms are admitted as boundary conditions. The representations of the twisted current algebras are studied their mass spectra match perfectly their fermionic realizations. The supersymmetric solutions are characterized and classified. A few especial ones are identified with Z₄, and Z₃ orbifolds by using the equality of the fermion equivalents