  We discuss tilting modules of affine quasi-hereditary algebras. We present an
existence theorem of indecomposable tilting modules when the algebra has a
large center and use it to deduce a criterion for an exact functor between two
affine highest weight categories to give an equivalence. As an application, we
prove that the Arakawa-Suzuki functor [Arakawa-Suzuki, J. of Alg. 209 (1998)]
gives a fully faithful embedding of a block of the deformed BGG category of
$\mathfrak{gl}_{m}$ into the module category of a suitable completion of
degenerate affine Hecke algebra of $GL_{n}$.
