  The goal of this paper is extend Kottwitz's theory of $B(G)$ for global
fields. In particular, we show how to extend the definition of ``$B(G)$ with
adelic coefficients'' from tori to all connected reductive groups. As an
application, we give an explicit construction of certain transfer factors for
non-regular semisimple elements of non-quasisplit groups. This generalizes some
results of Kaletha and Taibi. These formulas are used in the stabilization of
the cohomology of Shimura and Igusa varieties.
