  The special fiber of the local model of a PEL Shimura variety with
Iwahori-type level structure admits a cellular decomposition. The set of strata
is in a natural way a finite subset of the affine Weyl group determined by the
Shimura data. In this paper, we generalize and give a new proof of a theorem of
Kottwitz and Rapoport concerning the description of this set for the case of
linear and symplectic groups. For higher rank groups not of type A_n, we
produce counterexamples showing the situation is not as nice in general. Also,
we recover a theorem of Deodhar characterizing the Bruhat order on S_n.
