Triangulated categories of periodic complexes and orbit categories

We investigate the triangulated hull of orbit categories perfect derived category and bounded a ring concerning power suspension functor. It turns out that will correspond to full subcategory compact objects certain periodic complexes. This specializes Stai Zhao's result when is finite dimensional algebra with global dimension over field. As first application, if $A,B$ are flat algebras commutative they equivalent, then corresponding $n$-periodic complexes triangle equivalent. second we get version Koszul duality.