  Rosso and Green have shown how to embed the positive part $U_q(n)$ of a
quantum enveloping algebra $U_q(g)$ in a quantum shuffle algebra. In this paper
we study some properties of the image of the dual canonical basis $B^*$ of
$U_q(n)$ under this embedding $\Phi$. This is motivated by the fact that when
$g$ is of type $A_r$, the elements of $\Phi(B^*)$ are $q$-analogues of
irreducible characters of the affine Iwahori-Hecke algebras attached to the
groups $GL(m)$ over a $p$-adic field.
