For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification \bar{G}, which is a smooth Fano G \times G-variety of Picard number n enjoying many interesting properties. In this paper, it is shown that the wonderful compactification \bar{G} is rigid under Fano deformations. Namely, for any family of smooth Fano varieties over a connected base, if one fiber is isomorphic to \bar{G}, then so are all other fibers. This is a joint work with Qifeng Li.

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