We give complete descriptions of the tracial states on both the universal and reduced crossed products of a C*-dynamical system consisting of a unital C*-algebra and a discrete group. In particular, we also answer the question of when the tracial states are in canonical bijection with the invariant tracial states on the original C*-algebra. This generalizes the unique trace property for discrete groups. The analysis simplifies greatly in various cases, for example when the conjugacy classes of the original group are all finite, and in other cases gives previously known results, for example when the original C*-algebra is commutative. We also obtain results and examples in the case of abelian groups that contradict existing results in the literature of Bédos and Thomsen. Specifically, we give a finite-dimensional counterexample, and provide a correction to the result of Thomsen.

我们给出了由单位 C*-代数和离散群组成的 C*-动力系统的全称和约简交叉积的轨迹状态的完整描述。特别地，我们还回答了轨迹状态何时与原始 C*-代数上的不变轨迹状态处于正则双射的问题。这概括了离散组的独特跟踪属性。分析在各种情况下大大简化，例如当原始群的共轭类都是有限的时，而在其他情况下给出先前已知的结果，例如当原始 C*-代数是可交换的时。我们还获得了与 Bédos 和 Thomsen 文献中现有结果相矛盾的阿贝尔群的结果和例子。具体来说，我们给出一个有限维的反例，