  Let $F$ be a p-adic local field and $G=GL_2(F)$. Let $\mathcal{H}^{(1)}$ be
the pro-p Iwahori-Hecke algebra of $G$ with coefficients in an algebraic
closure of $\mathbb{F}_p$. We show that the supersingular irreducible
$\mathcal{H}^{(1)}$-modules of dimension 2 can be realized through the
equivariant cohomology of the flag variety of the mod p Langlands dual group of
$G$.
