Relative BGG sequences; II. BGG machinery and invariant operators

Applying this machinery to a specific compressable invariant differential operator of order one, we obtain a relative version of BGG (Bernstein-Gelfand-Gelfand) sequences. All our constructions apply in the case P=G, producing new and simpler proofs in the case of standard BGG sequences. We characterize cases in which the relative BGG sequences are complexes or even fine resolutions of certain sheaves and describe these sheaves. We show that this gives constructions of new invariant differential operators as well as of new subcomplexes in certain curved BGG sequences. The results are made explicit in the case of generalized path geometries.