\(K\)-theory of toric varieties revisited (Q2255526)

From the author's abstract: ``After surveying higher \(K\)-theory of toric varieties, we present Totaro's old (c.\ 1997) unpublished result (see \textit{B. Totaro} [Forum Math. Sigma 2, Article ID e17, 25 p. (2014; Zbl 1329.14018)]) on expressing the corresponding homotopy theory via singular cohomology. It is a higher analog of the rational Chern character isomorphism for general toric schemes. In the special case of a projective simplicial toric scheme over a regular ring one obtains a rational isomorphism between the homotopy K-theory and the direct sum of \(m\) copies of the \(K\)-theory of the ground ring, \(m\) being the number of maximal cones in the underlying fan.''