Bondal–Orlov fully faithfulness criterion for Deligne–Mumford stacks

Semiorthogonal decomposition of $\mathrm{D}^b(\mathrm{Bun}_2^L)$

“…To prove the fully-faithfulness we need to invoke the celebrated Bondal-Orlov criterion for fully-faithfulness which reduces the proof to computation of the cohomology of certain vector bundles. The original version was proved in [5], which already satisfy our need, if we want to work canonically with twisted sheaves we may use the generalization proved in [20].…”