In this paper, we construct incomplete versions of the equivariant stable category; that is, equivariant stabilizations of the category of $G$-spaces with respect to incomplete systems of transfers encoded by an $N_{\infty }$ operad $\mathcal{O}$. These categories are built from the categories of $\mathcal{O}$-algebras in $G$-spaces. Using this operadic formulation, we establish incomplete versions of the usual structural properties of the equivariant stable category, notably the tom Dieck splitting. Our work is motivated in part by the examples arising from the equivariant units and Picard space functors.

中文翻译：

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不完全转移系统的等变稳定范畴

在本文中，我们构造了等变稳定类别的不完整版本；也就是说，类别的等变镇定$G$-关于由一个编码的不完整传输系统的空间 $N_{\infty }$ 操作数 $\mathcal{哦}$. 这些类别是从以下类别构建的$\mathcal{哦}$-代数 $G$-空格。使用这个操作公式，我们建立了等变稳定类别的通常结构特性的不完整版本，特别是 tom Dieck 分裂。我们的工作部分是由等变单位和皮卡德空间函子产生的例子推动的。