  This paper contains a detailed exposition of the content of section five in
Kakde's paper arXiv:1008.0142. We proceed in a slightly more axiomatic way to
pin down the exact requirements on the $p$-adic Lie group under consideration.
We also make use of our conceptual theory of the completed localization of an
Iwasawa algebra as developed in arXiv:0711.2669. This simplifies some of the
arguments. Otherwise, with the exception of the notation at certain places, we
follow Kakde's paper.
