  The goal of this paper is to relate the quantum category $\mathcal{O}$ (known
also as the category of modules over the mixed quantum group) at an odd root of
unity to the affine Hecke category. Namely, we prove equivalences of highest
weight categories between integral blocks of the affine category $\mathcal{O}$
and the heart of the so called ``new'' t-structure on the affine Hecke
category. In order to do this we deform our categories over the formal
neighborhood of $0$ in the dual affine Cartan and show that the categories of
standardly filtered objects in the deformations are equivalent. For this, we
construct functors from the deformed categories to the category of bimodules
over the formal power series on the affine Cartan. Then we use what we call the
Rouquier-Soergel theory, also developed in this paper, to show that on the
categories of standardly filtered objects, these functors are full embeddings
with the same image.
