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