The conjectural bijection in 10.8 is proved in

Bezrukavnikov: Quasi-exceptional sets and  equivariant coherent sheaves
on the nilpotent cone, Represent.Th.7(2003)

with an important contribution by
Ostrik: On the equivariant K-theory of the nilpotent cone, 
Represent.Th.4(2000).

A weaker form of Conjecture 10.5 is proved in

Bezrukavnikov, Ostrik: On tensor categories attached to cells in affine Weyl 
groups II, in Adv.Studies Pure Math.40 Mat.Soc.Japan 2004.

For type A, Conjecture 10.5 is proved in 

Xi, The based ring of two-sided cells of affine Weyl groups of type A_{n-1}.
Mem.Amer.Math.Soc. 157(2002).