  We analyze the algebraic structures of G--Frobenius algebras which are the
algebras associated to global group quotient objects. Here G is any finite
group. These algebras turn out to be modules over the Drinfeld double of the
group ring k[G]. We furthermore prove that discrete torsion is a universal
group action of H^2(G,k^*) on G--Frobenius algebras by isomorphisms of the
underlying linear structure. These morphisms are realized explicitly by taking
the tensor product with twisted group rings. This gives an algebraic
realization of discrete torsion and allows for a treatment analogous to the
theory of projective representations of groups, group extensions and twisted
group ring modules. Lastly, we identify another set of discrete universal
transformations among G--Frobenius algebras pertaining to their
super--structure and classified by Hom(G,Z/2Z).
