Compactification of symmetric varieties

The symmetric varieties considered in this paper are the quotients G/H, where G is an adjoint semi-simple group over a field k of characteristic not equal 2, and H is the fixed point group of an involutorial automorphism of G which is defined over k. In the case k = C, De Concini and Procesi (1983) constructed a "wonderful" compactification of G/H. We prove the existence of such a compactification for arbitrary k. We also prove cohomology vanishing results for line bundles on the compactification.