  We show that the convolution algebra $K^G(\mathcal{B} \times \mathcal{B})$ is
isomorphic to the Based ring of the lowest two-sided cell of the extended
affine Weyl group associated to $G$, where $G$ is a connected reductive
algebraic group over the field $\mathbb{C}$ of complex numbers and
$\mathcal{B}$ is the flag variety of $G$.
