## Kunneth formula for graded rings associated to $K$-theories of Rost motives

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## Abstract:

In this paper, we study the graded ring $gr^*(X)$ defined by $K$-theory of a twist flag variety $X$. In particular, the Kunneth map $gr^*(R’)\otimes gr^*(R’)\to gr^*(R)$ is studied explicitly for an original Rost motive $R’$ and a generalized Rost motive $R$. Using this, we give examples $Tor(X)^2\not =0$ for the ideal $Tor(X)$ of torsion elements in the Chow ring $CH^*(X)$.## References

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## Additional Information

**Nobuaki Yagita**- Affiliation: Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
- MR Author ID: 185110
- Email: nobuaki.yagita.math@vc.ibaraki.ac.jp
- Received by editor(s): June 14, 2018
- Published electronically: July 1, 2019
- Communicated by: Mark Behrens
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4513-4526 - MSC (2010): Primary 57T15, 20G15, 14C15
- DOI: https://doi.org/10.1090/proc/14622
- MathSciNet review: 4002560