Proposition 2.10 is false as stated. The problem is that in the proof we implicitely consider the image of H(W, u) inside the algebra tensored by K, which kills the torsion. Thus the statement must be modified to:

“Then the non-torsion part of H(W, u) satisfies (a) and (b) of conjecture 2.2, and {T_{w} | w ∈ W} is an A-basis of this non-torsion part.”