Abstract For a proper, cocompact action by a locally compact group of the form H × G , with H compact, we define an H × G -equivariant index of H -transversally elliptic operators, which takes values in K K ∗ ( C ∗ H , C ∗ G ) . This simultaneously generalises the Baum–Connes analytic assembly map, Atiyah’s index of transversally elliptic operators, and Kawasaki’s orbifold index. This index also generalises the assembly map to elliptic operators on orbifolds. In the special case where the manifold in question is a real semisimple Lie group, G is a cocompact lattice and H is a maximal compact subgroup, we realise the Dirac induction map from the Connes–Kasparov conjecture as a Kasparov product and obtain an index theorem for Spin-Dirac operators on compact locally symmetric spaces.

中文翻译：

---

适当动作的等变orbifold索引

摘要 对于由 H × G 形式的局部紧群进行的适当的协紧作用，对于 H 紧凑，我们定义了 H × G - 横向椭圆算子的 H × G -等变指数，其取值 KK ∗ ( C ∗ H , C*G)。这同时概括了 Baum-Connes 分析装配图、Atiyah 的横向椭圆算子指数和 Kawasaki 的 orbifold 指数。该索引还将装配图推广到轨道上的椭圆算子。在所讨论的流形是实半单李群、G 是共紧格、H 是极大紧子群的特殊情况下，我们将康涅斯-卡斯帕罗夫猜想的狄拉克归纳图实现为卡斯帕罗夫乘积，并获得指数定理用于紧凑局部对称空间上的自旋狄拉克算子。