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. txt, pp. 1–44 constructed a wonderful compactification of any symmetric variety given by a quotient G/G^{\sigma} of an algebraic group G by the subgroup G^{\sigma} fixed by some involution \sigma of G over the complex numbers, sometimes called the De Concini–Procesi compactification. txt generalized this construction to arbitrary characteristic. In particular, by writing a group G itself as a symmetric homogeneous space, G=(G \times G)/G (modulo the diagonal subgroup), this gives a wonderful compactification of the group G itself.

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