Twisted geometric Satake equivalence

Let k be an algebraically closed field and O = k[[t]] F = k((t)). For an almost simple algebraic group G we classify central extensions 1 →G _m→ E →G (F) 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character : N(K) ℚell;^* (under some assumption on the characteristic of k). Consider the category of G(O)-bi-invariant perverse sheaves on E with Gm-monodromy . We show that this is a tensor category, which is tensor equivalent to the category of representations of a reductive group E,N. We compute the root datum of E,N.