Abstract We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.

中文翻译：

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相对等变动机和模块

摘要 我们介绍并研究了（versal）标志变体的各种（等变）动机类别。我们将这些类别与某些类别的抛物线 (Demazure) 模块相关联。我们表明，versal 标志品种的动机分解类型取决于抛物线模块的直接和分解类型。为此，我们在广义定向上同调的上下文中使用 Kostant 和 Kumar 的定位技术以及代数协边主义及其泛型版本的 Rost 幂零原理。作为一个应用程序，我们获得了versal flag 品种不可分解的Chow 动机的新证明和例子。