Algebraic groups and motives of projective homogeneous varieties of outer type

动机的概念是现代代数几何的基础。最初，它是由亚历山大格罗滕迪克介绍的，试图统一上同调理论。同时动机成为一个主要的语言在代数几何制定和解决其问题。我们调查的主题是代数群在任意领域的重点是群体的外部类型，齐次品种，和他们的周动机。我们的主要目标包括齐次簇的motivic分解，离散motivic不变量，研究齐次簇上的代数圈和群与torsors的上同调不变量。

The concept of motive is fundamental in modern algebraic geometry. Originally it was introduced by Alexander Grothendieck as an attempt to unify cohomology theories. Meanwhile motives became one of the main languages in algebraic geometry to formulate and to solve its problems. The subject of our investigations are algebraic groups over arbitrary fields with a focus on groups of outer type, homogeneous varieties, and their Chow motives. Our main goals include motivic decompositions of homogeneous varieties, discrete motivic invariants, study of algebraic cycles on homogeneous varieties and cohomological invariants of groups and torsors.