In this paper, we will use the splitting of the Frobenius direct image of line bundles on toric varieties to explicitly construct an orthogonal basis of line bundles in the derived category $D^b(X)$ where $X$ is a Fano toric variety with (almost) maximal Picard number.
"Frobenius splitting and derived category of toric varieties." Illinois J. Math. 54 (2) 649 - 669, Summer 2010. https://doi.org/10.1215/ijm/1318598676