  Let G be a complex algebraic semi-simple adjoint group and X a smooth
complete symmetric G-variety. Let L_i be the irreducible G-equivariant
intersection cohomology complexes on X, and L the direct sum of the L_i. Let E=
Ext(L,L) be the extension algebra of L, computed in the G-equivariant derived
category of X. We considered E as a dg-algebra with differential d=0, and the
E_i = Ext(L,L_i) as E-dg-modules. We show that the bounded equivariant derived
category of sheaves of C-vector spaces on X is equivalent to the subcategory of
the derived category of E-dg-modules generated by the E_i.
