Affine quantum groups and Steinberg varieties of type C

We provide a geometric realization of the quasi-split affine quantum group of type AIII₂ₙ₋₁(τ) in terms of equivariant K-groups of non-connected Steinberg varieties of type C. This uses a new Drinfeld type presentation of this affine quantum group which admits very nontrivial Serre relations. We then construct \`a la Springer a family of finite-dimensional standard modules and irreducible modules of this quantum group, and provide a composition multiplicity formula of the standard modules.