  The uniform tracial completion of a C*-algebra A with compact non-empty trace
space T(A) is obtained by completing the unit ball with respect to the uniform
2-seminorm $\|a\|_{2,T(A)}=\sup_{\tau \in T(A)} \tau(a^*a)^{1/2}$. The trace
problem asks whether every trace on the uniform tracial completion is the
$\|\cdot\|_{2,T(A)}$-continuous extension of a trace on A. We answer this
question positively in the case of C*-algebras that tensorially absorb the
Jiang-Su algebra, such as those studied in the Elliott classification
programme.
