Let k be an algebraically closed field of characteristic p and G be a finite group. Let N be a normal subgroup of G and c be a G-stable block of kN. We shall discuss the cohomology algebra of the block c, defined by M. Linckelmann and, in this case a generalized block cohomology which can be defined using some generalized Brauer pairs, denoted (c, G)-Brauer pairs, which are introduced by R. Kessar and R. Stancu. We also analyze the restriction map