We show that there exists a n-tilting module T' equivalent to T which induces a derived equivalence between the unbounded derived category D(R) and the triangulated subcategory of D(End(T')) consisting of the E-local objects, where E is the kernel of the total left derived functor of the tensor product with T' over End(T'). In case T is a classical n-tilting module, we get again the Cline-Parshall-Scott and Happel's results.

This is a joint work with Bazzoni and Mantese.