  We explain how quantum affine algebra actions can be used to systematically
construct "exotic" t-structures. The main idea, roughly speaking, is to take
advantage of the two different descriptions of quantum affine algebras, the
Drinfeld--Jimbo and the Kac--Moody realizations.
  Our main application is to obtain exotic t-structures on certain convolution
varieties defined using the Beilinson--Drinfeld and affine Grassmannians. These
varieties play an important role in the geometric Langlands program, knot
homology constructions, K-theoretic geometric Satake and the coherent Satake
category. As a special case we also recover the exotic t-structures of
Bezrukavnikov--Mirkovic on the (Grothendieck--)Springer resolution in type A.
