  We use Drinfeld style generators and relations to define an algebra
$\mathfrak{U}_n$ which is a "$q=0$" version of the affine quantum group of
$\mathfrak{gl}_n.$ We then use the convolution product on the equivariant
$K$-theory of spaces of pairs of partial flags in a $d$-dimensional vector
space $V$ to define affine zero-Schur algebras ${\mathbb
S}_0^{\operatorname{aff}}(n,d)$ and to prove that for every $d$ there exists a
surjective homomorphism from $\mathfrak{U}_n$ to ${\mathbb
S}_0^{\operatorname{aff}}(n,d).$
