  We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a
reductive algebraic group G defined and split over a non-archimedean local
field K. Following their lines, we prove that the generalized Steinberg
representations of G with coefficients in any abelian group are cyclic. When G
is semi-simple of adjoint type, we give an expression of these representations,
whenever it is possible and in particular for those that are of maximal degree,
in terms of the parahoric subgroups of G.
