  We determine the Ringel duals for all blocks in the parabolic versions of the
BGG category O associated to a reductive finite dimensional Lie algebra. In
particular we find that, contrary to the original category O and the specific
previously known cases in the parabolic setting, the blocks are not necessarily
Ringel self-dual. However, the parabolic category O as a whole is still Ringel
self-dual.
  Furthermore, we use generalisations of the Ringel duality functor to obtain
large classes of derived equivalences between blocks in parabolic and original
category O. It seems that only some special cases were known thus far, where
the proof relied purely on a geometric approach to category O. We subsequently
classify all derived equivalence classes of blocks of category O in type A
which preserve the Koszul grading.
