On the strongly regular locus of the inertia stack of $\mathrm{Bun}_{G}$

Let G be a connected reductive group over a finite extension of \mathbb{Q}_{p} . We show that for each b\in B(G) , the strongly regular locus of the inertia stack of \mathrm{Bun}_{G}^{b} is open in the inertia stack of \mathrm{Bun}_{G} . As a consequence, we extend the computation of Hansen–Kaletha–Weinstein of trace distributions of the cohomology of local shtuka spaces \mathrm{Sht}_{G,b,\mu} to non-basic b . If b is closed in B(G,\mu) , or b is basic and has only one specialization in B(G,\mu) , 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.