Affine Deligne-Lusztig varieties in affine flag varieties
  This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method. 
Ulrich Goertz, Thomas J. Haines, Robert E. Kottwitz, Daniel C. Reuman