  In this paper we give a geometric construction of Cherednik's double affine
Hecke algebra.
  We construct the algebra as the equivariant $K$-theory of the Lagrangian
subvariety of the cotangent variety of the square of the flag variety of $G$,
the variety being given by the union of the conormal bundles to the $G$-orbits
on $\flag\times\flag$.
  This is a generalisation of work of Kazhdan and Lusztig to the Kac-Moody
case, and is suitable for describing a certain class of modules for this
algebra. In a paper in preparation we will do this, in the case $G$ is affine
(Cherednik's case).

Quantum Algebra;Quantum Algebra