Traces on the cone algebra with asymptotics

For every singular point on a manifold with conical singularities we construct a trace on the 'Cone Algebra with Asymptotics introduced by B.-W. Schulze. Each of these traces is determined at the singularity; none of them therefore is induced by WodzickPs noncommutative residue. On the ideal of operators with vanishing conormal symbol, however, we find another trace which coincides with the noncommutative residue in the interior. Moreover, it is shown that all these traces are essentially unique on a slightly extended version of the cone algebra. AMS Subject Classification: 58 G 15, 47 D 25, 46 H 35.