We classify the primitive idempotents of the $p$‐local complex representation ring of a finite group $G$ in terms of the cyclic subgroups of order prime to $p$ and show that they all come from idempotents of the Burnside ring. Our results hold without adjoining roots of unity or inverting the order of $G$, thus extending classical structure theorems. We then derive explicit group‐theoretic obstructions for tensor induction to be compatible with the resulting idempotent splitting of the representation ring Mackey functor.

中文翻译：

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K理论的幂等性和等倍分裂

我们将...的原始幂等分类 $p$-有限群的局部复数表示环 $G$ 就阶素的循环子群而言 $p$并证明它们都来自Burnside环的幂等。我们的结果保持不变，而没有邻接的统一根源或颠倒的顺序。$G$，从而扩展了经典结构定理。然后，我们得出张量归纳的显式群理论障碍，以与表示环Mackey函子的幂等分裂相兼容。