Derived Equivalence induced by $n$-tilting modules

Let $T_R$ be a right $n$-tilting module over an arbitrary associative ring $R$. In this paper we prove that there exists a $n$-tilting module $T_R^{\mathrm{\prime }}$ equivalent to $T_R$ which induces a derived equivalence between the unbounded derived category $\text{D}(R)$ and a triangulated subcategory ${\mathcal{E}}_{\perp }$ of $\text{D}(\text{End}(T^{\mathrm{\prime }}))$ equivalent to the quotient category of $\text{D}(\text{End}(T^{\mathrm{\prime }}))$ modulo the kernel of the total left derived functor $-{\otimes }_{S^{\mathrm{\prime }}}^{\mathbb{L}}{T}^{\mathrm{\prime }}$. In case $T_R$ is a classical $n$-tilting module, we get again the Cline-Parshall-Scott and Happel’s results.