  We construct categories of Harish-Chandra bimodules for affine Lie algebras
analogous to Harish-Chandra bimodules with infinitesimal characters for simple
Lie algebras, addressing an old problem raised by I. Frenkel and Malikov. Under
an integrality hypothesis, we establish monoidal equivalences between blocks of
our affine Harish-Chandra bimodules and versions of the affine Hecke category.
To do so, we introduce a new singular localization onto Whittaker flag
manifolds. The argument for the latter specializes to a somewhat alternative
treatment of regular localization, and identifies the category of Lie algebra
representations with a generalized infinitesimal character as the parabolic
induction, in the sense of categorical representation theory, of a Steinberg
module.
