  We prove a tamely ramified version of the Kazhdan-Lusztig equivalence using
factorization algebras. More precisely, we establish an equivalence between the
DG category of Iwahori-integrable affine Lie algebra representations and the DG
category of representations of the "mixed" quantum group. This confirms a
conjecture by D. Gaitsgory in arXiv:1810.09054 [math.RT].
