Global B(G) with adelic coefficients and transfer factors at non-regular elements

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.