  A theorem of Kazhdan and Lusztig establishes an equivalence between the
category of G(CO)-integrable representations of the Kac-Moody algebra
\hat{g}_{-\kappa} at a negative level -\kappa and the category \Rep_q(G) of
(algebraic) representations of the "big" (a.k.a. Lusztig's) quantum group. In
this paper we propose a conjecture that describes the category of
Iwahori-integrable Kac-Moody modules. The corresponding object on the quantum
group side, denoted Rep^{mxd}_q(G), involves Lusztig's version of the quantum
group for the Borel and the De Concini-Kac version for the negative Borel.
