  This is an application of the theory of tilting objects to the geometric
setting of perverse sheaves. We show that this theory is a natural framework
for Beilinson's gluing of perverse sheaves construction. In the special case of
Schubert stratification of a flag variety we get a short proof of Soergel's
"Struktursatz", and describe (following a conjecture of Kapranov) Serre functor
for category O. Some of our results were obtained independently by Rouquier.
