We will discuss a method for studying derived categories of geometric invariant theory quotients by constructing compactifications of group actions. This gives an explicit geometric realization of some fully-faithful functors which have been studied recently in several contexts (under the name "grade restriction windows") and reproduces some famous exceptional collections in a very direct way. Time permitting we may discuss some connections with some conjectural Bridgeland stability conditions suggested by the physics literature and wall-crossing equivalences.