A full exceptional collection on an algebraic variety is a kind of basis in its derived category of coherent sheaves. A long standing conjecture (proved by Kapranov for Dynkin type A) predicts the existence of full exceptional collections on projective homogeneous varieties of reductive algebraic groups over algebraically closed fields of characteristic zero. In this particular case the problem can be reformulated purely in terms of representation theory of the corresponding parabolic subgroup.\\ I will overview what is known in this direction and discuss recent progress.

First, I will discuss the connection between projective presentations of maximal rank and generically tau-regular components of module varieties. Then I will present some classification results for generically tau-regular components. This is joint work with Grzegorz Bobinski.