Summary: Let \(k\) be an algebraically closed field and \(O = \text{k}[[t]] \subset F = \text{k}((t))\). For an almost simple algebraic group \(G\) we classify central extensions \(1 \rightarrow \mathbb G_{m} \rightarrow E \rightarrow G(F) \rightarrow 1\); any such extension splits canonically over \(G(O)\). Fix a positive integer \(N\) and a primitive character \(\zeta : \mu_N(k) \rightarrow \bar{\mathbb Q}^*_{\ell}\) (under some assumption on the characteristic of k). Consider the category of \(G(O)\)-bi-invariant perverse sheaves on \(E\) with \(\mathbb G_{m}\)-monodromy \( \zeta\). We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group \(\check G_{E,N}\). We compute the root datum of \(\check G_{E,N}\).