ScalingStacks

Corollary 1.11. There is a canonical equivalence

$$\mathcal{Z}(\mathcal{H}_{G}^{\it{aff}})\simeq\qc(\mathcal{L}(\mathcal{L}BG))\simeq\qc((BG^{S^{1}})^{S^{1}})\simeq\qc({\mathcal{L}oc}_{G}(T^{2}))$$

between the center of the quasi-coherent affine Hecke $\infty$-category and the $\infty$-category of sheaves on the derived moduli stack of $G$-local systems on the torus.