Traces on cores of C∗-algebras associated with self-similar maps

We completely classify the extreme tracial states on the cores of the C∗-algebras associated with self-similar maps on compact metric spaces. We present a complete list of them. The extreme tracial states are the union of the discrete type tracial states given by measures supported on the finite orbits of the branch points and a continuous type tracial state given by the Hutchinson measure on the original self-similar set.