K-group, zeroth (Ex)

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  • Show that the group K_0(R) is isomorphic to the group obtain by applying the Grothendieck construction to the abelian monoid of isomorphism classes of finitely generated projective R-modules under direct sum.
  • Compute K_0(\Cc[S_3]), where S_3 is the symmetric group on three elements.
  • Show that the C(S^2)-module of sections of the tangent bundle TS^2 is finitely generated projective and even stably finitely generated free, but not finitely generated free.

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