On the strongly regular locus of the inertia stack of BunG

Let G be a connected reductive group over a finite extension of Qₚ . We show that for each b∈ B(G) , the strongly regular locus of the inertia stack of BunGᵇ is open in the inertia stack of BunG . As a consequence, we extend the computation of Hansen–Kaletha–Weinstein of trace distributions of the cohomology of local shtuka spaces ShtG,b,μ to non-basic b . If b is closed in B(G,μ) , or b is basic and has only one specialization in B(G,μ) , then we compute the trace distribution of the entire strongly regular locus. In the process, we prove some results on the behavior of characteristic classes under cohomologically smooth pullback.