  In this paper, we use Soergel calculus to define a monoidal functor, called
the evaluation functor, from extended affine type A Soergel bimodules to the
homotopy category of bounded complexes in finite type A Soergel bimodules. This
functor categorifies the well-known evaluation homomorphism from the extended
affine type A Hecke algebra to the finite type A Hecke algebra. Through it, one
can pull back the triangulated birepresentation induced by any finitary
birepresentation of finite type A Soergel bimodules to obtain a triangulated
birepresentation of extended affine type A Soergel bimodules. We show that if
the initial finitary birepresentation in finite type A is a cell
birepresentation, the evaluation birepresentation in extended affine type A has
a finitary cover, which we illustrate by working out the case of cell
birepresentations with subregular apex in detail.
