  Let G be a simple algebraic group over the complex numbers. Let N be the cone
of nilpotent elements in the Lie algebra of G. Let K_{G x C^*}(N) denote the
Grothendieck group of the category of G x C^*-equivariant coherent sheaves on
N. In this note we construct a Kazhdan-Lusztig type canonical basis of K_{G x
C^*}(N) over representation ring of C^*. This basis is parametrized by the set
of dominant weights for G. On the other hand we conjecture that this basis is
close to the basis consisting of irreducible G-equivariant bundles on nilpotent
orbits. This would give us a natural construction of Lusztig's bijection
between two sets: \{dominant weights for G\} and \{pairs consisting of a
nilpotent orbit O and irreducible G-equivariant bundle on O.
