Wonderful compactification

In algebraic group theory, a wonderful compactification of a variety acted on by an algebraic group G is a G-equivariant compactification such that the closure of each orbit is smooth. C. De Concini and C. Procesi (1983) constructed a wonderful compactification of any symmetric variety given by a quotient G/G^σ of an algebraic group G by the subgroup G^σ fixed by some involution σ of G over the complex numbers, sometimes called the De Concini–Procesi compactification, and Strickland (1987) generalized this to arbitrary characteristic. In particular, by writing a group G itself as a symmetric homogeneous space G=(G×G)/G (modulo the diagonal subgroup) this gives a wonderful compactification of the group G itself.