...(1) . . . c(l). Let M = ⊕l i=0(Πc(0)...c(i))(i). Then M is a tilting object in SubZΠw. In particular, we have a triangle equivalence Sub ZΠw ≃ K b(proj EndZΠw(M)). Remark 4.3. It was shown by Yamaura =-=[Y]-=- that, for a finite dimensional self-injective positively graded algebra A, the stable category modZA has a tilting object ⊕ i≥0(A(i))≤0 if A0 has finite global dimension. Our tilting object M in Sub ...