  Let G be a split semi-simple linear algebraic group over a field, let P be a
parabolic subgroup and let L be a line bundle on the projective homogeneous
variety G/P. We give a simple condition on the class of L in Pic(G/P)/2 in
terms of Dynkin diagrams implying that the Witt groups W^i(G/P,L) are zero for
all integers i. In particular, if B is a Borel subgroup, then W^i(G/B,L) is
zero unless L is trivial in Pic(G/B)/2.
