Bruhat-Tits decomposition and the Hasse principle

Let k be a number field, (k(v))(v is an element of Omega) the completions of k and G/k a semisimple group. Let us denote by H-1 (k(t), G) the pointed set of Galois cohomology for the field k(t). We study the kernel III1 (k(t), G) of the map H-1(k(t), G) --> Pi(v is an element of Omega) H-1 (k(v)(t), G) and we give sufficient conditions for the triviality of III(k(r), G).