Relative homology and maximal l-orthogonal modules

Let Λ be an artin algebra and let M1 and M2 be generator–cogenerators for modΛ, such that the global dimension of their endomorphism ring is finite. We characterize tilting modules of the form HomΛ(M2,M1) with respect to the relative theories induced by M1 and M2 on modΛ and apply our results to maximal l-orthogonal modules.