On group rings of linear groups

Let H be a finitely generated group of matrices over a field F of characteristic zero. We consider the group ring KH of H over an arbitrary field K whose characteristic is either zero or greater than some number N = N ( H ) . We prove that KH is isomorphic to a subring of a ring S which is a crossed product of a division ring Δ with a finite group. Hence KH is isomorphic to a subring of a matrix ring over a skew field.