When do reduced Whitehead groups of Iwasawa algebras vanish? A reduction step

Let l be an odd prime and K/k a Galois extension of totally real fields with Galois group G such that K/k∞ and k/Q are finite. We reduce the conjectured triviality of the reduced Whitehead group SK1(QG) of the algebra QG=Quot(ΛG) with the Iwasawa algebra ΛG=Zl[[G]] to the case of pro-l Galois groups G and finite unramified coefficient extensions.