The endoscopic transfer factor is expressed as difference of characters for the even and odd parts of the spin modules, or Dirac index of the trivial representation. The lifting of tempered characters in terms of index of Dirac cohomology is calculated explicitly.

中文翻译：

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狄拉克上同调和字符提升

内窥镜传递因子表示为自旋模块的偶数和奇数部分的特征差异，或平凡表示的狄拉克指数。明确计算了在狄拉克上同调指数方面钢化字符的提升。