Torsion in CH2 of Severi-Brauer varieties and indecomposability of generic algebras

We compute degrees of algebraic cycles on certain Severi-Brauer varieties and apply it to show that:

–	- a generic division algebra of indexp α and exponentp is not decomposable (in a tensor product of two algebras) for any primep and any α except the case whenp=2 and 2 | α;
–	- the 2-codimensional Chow group CH2 of the Severi-Brauer variety corresponding to the generic division algebra of index 8 and exponent 2 has a non-trivial torsion.

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