%0 Journal Article %T From conjugacy classes in the Weyl group to unipotent classes, III %A G. Lusztig %J Mathematics %D 2011 %I arXiv %X Let G be an affine algebraic group over an algebraically closed field such that the identity component G^0 of G is reductive. Let W be the Weyl group of G and let D be a connected component of G whose image in G/G^0 is a unipotent element. In this paper we define a map from the set of "twisted conjugay classes" in W to the set of unipotent G^0-conjugacy classes in D, generalizing an earlier construction which applied when G is connected. %U http://arxiv.org/abs/1104.3112v2