  Let R be a Dedekind domain, and let G be a simply connected
Chevalley-Demazure group scheme of rank =>2. We prove that
G(R[x_1,...,x_n])=G(R)E(R[x_1,...,x_n]) for any n=>1. This extends the
corresponding results of A. Suslin and F. Grunewald, J. Mennicke, and L.
Vaserstein for G=SL_n, Sp_2n. We also deduce some corollaries of the above
result for regular rings R of higher dimension and discrete Hodge algebras over
R.
