  Let G be a unitary group over a totally real field, and X a Shimura variety
for G. For certain primes p of good reduction for X, we construct cycles on the
characteristic p fiber of X. These cycles are defined as the loci on which the
Verschiebung map has small rank on particular pieces of the Lie algebra of the
universal abelian variety on X.
  The geometry of these cycles turns out to be closely related to Shimura
varieties for a different unitary group G', which is isomorphic to G at finite
places but not isomorphic to G at archimedean places. More precisely, each such
cycle has a natural desingularization, and this desingularization is "almost"
isomorphic to a scheme parametrizing certain subbundles of the Lie algebra of
the universal abelian variety over a Shimura variety X' arising from G'.
  We exploit this relationship to construct an injection of the etale
cohomology of X' into that of X. This yields a geometric construction of
"Jacquet-Langlands transfers" of automorphic representations of G' to
automorphic representations of G.
