Torsors of isotropic reductive groups over Laurent polynomials

Let k be a field of characteristic 0. G reductive group over the ring Laurent polynomials R=k[x_1^{\pm 1},...,x_n^{\pm 1}]. We prove that has isotropic rank >=1 R iff it fractions k(x_1,...,x_n) R, and if this is case, then natural map H^1_{et}(R,G)\to H^1_{\et}(k(x_1,...,x_n),G) trivial kernel, loop reductive, i.e. contains maximal R-torus. In particular, we settle in positive conjecture V. Chernousov, P. Gille, A. Pianzola H^1_{Zar}(R,G)=* for such groups G. also deduce >=2, non-stable K_1-functors K_1^G(R)\to K_1^G( k((x_1))...((x_n)) ) injective, an isomorphism moreover semisimple.