  Let G be the group of F-points of a reductive group defined over F, $\sigma$
a rational involution of this group defined over F and H the group of fixed
points of $\sigma$ . We built rational families of H-fixed vectors in the dual
of generalized principal series, using smooth homology of groups. Results of
A.G.Helminck,S.P.Wang and A.G.Helminck,G.F.Helminck on the structure of
$\mathbb F$-varieties are also essential.
