It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological spaces has an algebraic analogue in the module category of a ring. Inspired by the work of Eckmann-Hilton, various authors studied the problem of constructing a homotopy theory in more general algebraic categories. We refer to the works of Heller [18], [20], [19], Huber [23], Kleisli [29], Brown [12], Auslander-Bridger [1] and Quillen [35]. Restricting to the case of a module category, there are two different in general, homotopy theories defined. The injective homotopy which is defined by killing the injective modules and the projective homotopy which is defined by killing the projective modules. Let � be an associative ring, and let Mod(�) be the category of right � -modules. Using injective homotopy we obtain the stable category Mod(�) which is always right triangulated, and using projective homotopy we obtain the stable category Mod(�) which is always left triangulated. The projective and the injective homotopy coincide iff the ring is Quasi-Frobenius (QF-ring for short) and in this case the stable category Mod(�) = Mod(�) is a compactly generated triangulated category. The stable module category of a modular group algebra (which is a QF-ring), has been studied by many authors mainly from the representation theoretic point of view. There is recently a big progress in this study, which is developed using machinery from the theory of triangulated categories, in particular Bousfield’s localization techniques, see for example [36], [11]. Our main purpose in this paper is to study the stable module cat