Complex K-theory of complex projective space
= Complex K-theory of complex projective space
{c}
{title2=$K^0(\mathbb{CP}^n)$}
If $t=1-[\overline\gamma]$ for the tautological complex line bundle, then
$$
K^0(\mathbb{CP}^n)\cong\mathbb Z[t]/(t^{n+1}),
\qquad
K^{-1}(\mathbb{CP}^n)=0.
$$