Let R be a Dedekind domain and G a split reductive group, i.e. a Chevalley-Demazure group scheme, of rank ≥ 2 {geq 2}. We prove that G ? (R ? [ x 1, ..., x n ]) = G ? (R) ? E ? (R ? [ x 1, ..., x n ]) ? for any ? n ≥ 1. G(R[x-{1},ldots,x-{n}])=G(R)E(R[x-{1},ldots,x-{n}])quadtext{for any} n% geq 1. In particular, this extends to orthogonal groups the corresponding results of A. Suslin and F. Grunewald, J. Mennicke and L. Vaserstein for G = SL N, Sp 2 ? N {G=mathrm{SL}-{N},mathrm{Sp}-{2N}}. We also deduce some corollaries of the above result for regular rings R of higher dimension and discrete Hodge algebras over R.