Equivariant cohomology of the wonderful group compactification

In this paper we compute the rational G×G-equivariant cohomology ring of the so-called wonderful compactification of G (see [C. de Concini, C. Procesi, Complete symmetric varieties, in: Invariant Theory, Montecatini, 1982, in: Lecture Notes in Math., vol. 996, Springer-Verlag, Berlin, 1983, pp. 1–44]). This is obtained as an application of the results in [E. Bifet, C. de Concini, C. Procesi, Cohomology of regular embeddings, Adv. Math. 82 (1) (1990) 1–34; E. Strickland, Computing the equivariant cohomology of group compactifications, Math. Ann. 291 (2) (1991) 275–280] by a careful analysis of the relevant Stanley–Reisner systems.