  We study projective functors (i.e. direct summands of compositions of
translations through walls) for parabolic versions of $\cO$ as well as for
integral regular blocks outside the critical hyperplanes in the symmetrizable
Kac-Moody case. It turns out that in both situations the functors are
completely determined by their restriction to the additive category generated
by (the limit of) a `full projective tilting' object. We describe how
projective functors in the parabolic setup give rise to an invariant of tangle
cobordisms and formulate a conjectural direct connection to Khovanov homology.
Our main result, however, is the classification theorem for indecomposable
projective functors in the Kac-Moody case verifying a conjecture of F. Malikov
and I. Frenkel.
