On the affineness of Deligne–Lusztig varieties

We prove that the Deligne–Lusztig variety associated to minimal length elements in any δ-conjugacy class of the Weyl group is affine, which was conjectured by Orlik and Rapoport in [S. Orlik, M. Rapoport, Deligne–Lusztig varieties and period domains over finite fields, arXiv: 0705.1646].