Recently, two of the authors of this paper constructed cyclic cocycles on Harish–Chandra’s Schwartz algebra of linear reductive Lie groups that detect all information in the K-theory of the corresponding group \(C^*\)-algebra. The main result in this paper is an index formula for the pairings of these cocycles with equivariant indices of elliptic operators for proper, cocompact actions. This index formula completely determines such equivariant indices via topological expressions.

中文翻译：

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高轨道积分的指数定理

最近，本文的两位作者在线性还原李群的 Harish-Chandra 的 Schwartz 代数上构造了循环余环，该代数检测了对应群\(C^*\)代数的K理论中的所有信息。本文的主要结果是这些共环与椭圆算子的等变指数配对的指数公式，以实现适当的协紧行动。这个指标公式完全通过拓扑表达式确定了这样的等变指标。