1)), i.e. is there a space whose homology is the Rost motive? 2. Is there an algebraic analogue of (4.4) and if yes, what is the algebraic analogue n...

1)), i.e. is there a space whose homology is the Rost motive? 2. Is there an algebraic analogue of (4.4) and if yes, what is the algebraic analogue n of 2 (1) KR(n)? 3. Is there a M GL-module decomposition of M GL X for a Pster quadric X analogous to the motivic decomposition constructed by Rost [24]? 4. Is there an algebraic analogue of S(2n ), and is there a meaningful algebraic analogue of the Hopf invariant 1 problem as stated at the end of last section?