Bott periodicity and calculus of Euler classes on spheres

A variety of computations regarding the Euler class group E(An,An) and the Grothendieck group K0(An) of the algebraic sphere Spec(An) is done. The Euler class of the algebraic tangent bundle on Spec(An) is computed. It is also investigated whether every element in the Euler class group E(An,An) is the Euler class of a projective An module of rank n.