A comparison between cohomology and \(K\)-theory of weighted projective spaces (Q1323653)

In [ibid., 113-127 (1994; see the review above)] the author computed the complex \(K\)-theory ring of \(P^ n_ \mathbb{C} (q_ 0,\dots, q_ n)\), the weighted projective space which is the quotient of \(\mathbb{C}^{n + 1} - \{0\}\) by the \(\mathbb{C}^*\)-action given by \(\lambda (\tau_ 0, \dots, \tau_ n) = (\lambda^{q_ 0} \tau_ 0, \dots, \lambda^{q_ n} \tau_ n)\). In this sequel he gives another calculation, which works only under restrictions on the \(\{q_ i\}\). The method, when it works, shows that \(K^*(P^ n_{\mathbb{C}} (q_ 0, \dots, q_ n))\) is isomorphic to the cohomology ring.