In algebraic group theory, a wonderful compactification of a variety acted on by an algebraic group formula_1 is a formula_1-equivariant compactification such that the closure of each orbit is smooth. Corrado de Concini and Claudio Procesi (1983) constructed a wonderful compactification of any symmetric variety given by a quotient formula_3 of an algebraic group formula_1 by the subgroup formula_5 fixed by some involution formula_6 of formula_1 over the complex numbers, sometimes called the De Concini–Procesi compactification, and Elisabetta Strickland (1987) generalized this construction to arbitrary characteristic. In particular, by writing a group formula_1 itself as a symmetric homogeneous space, formula_9 (modulo the diagonal subgroup), this gives a wonderful compactification of the group formula_1 itself.