Traces on the uniform tracial completion of Z-stable C*-algebras

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)=τ ∈ T(A) τ(a^*a)1/2. The trace problem asks whether every trace on the uniform tracial completion is the \|·\|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.