  We describe the group SK_1(R[G]) for group rings R[G] where G is an arbitrary
finite group and where the coefficient ring R is a p-adically complete
Noetherian integral domain of characteristic zero which admits a lift of
Frobenius and which also satisfies a number of further mild conditions. Our
results extend previous work of R. Oliver who obtained such results for the
valuation rings of finite extensions of the p-adic field.
