Where can I find any more or less explicit semi-orthogonal decompositions of derived categories of perfect complexes or of bounded derived categories for singular schemes that are proper over a ring R?

I guess that one can take a "Beilinson-type" decomposition of $D^{perf}(\mathbb{P}^n(\operatorname{Spec}\,R))$ where $R$ is not regular; one can probably take the "inverse image" of this decomposition to something like $D^{perf}(\mathbb{P}^n\times V(\operatorname{Spec}\,R))$. Yet I would like to have some references for this argument. Moreover, I would like to find some "more interesting" examples. This question is certainly related to examples of explicit descriptions of derived categories of singular varieties.