Let \(X\) be a scheme over a field \(k\) which admits an ample line bundle and \(\text{vec}(X)\) the category of algebraic vector bundles on \(X\).
As announced by the author [B. Keller, J. Pure Appl. Algebra 136, No. 1, 1-56 (1999)], he shows that the cyclic homology \(HC_\ast(X)\) of \(X\) coincides with the cyclic homology \(HC_\ast^{\text{der}} (\text{vec}(X))\) of the category \(\text{vec}(X)\). Then, a new construction of the Chern character of a perfect complex on a ringed space is presented.