Frobenius contraction of \(G\)-modules (Q424848)

Using the newly found splitting of the Frobenius endomorphism on the algebra of distributions of a simply connected semisimple algebraic group \(G\) over an algebraically closed field of positive characteristic, the authors give a new proof of the Frobenius splitting of the flag variety of \(G\) and of its \(G\)-equivariant nature (originally splitting of this flag variety has been proved by \textit{V. B. Mehta} and \textit{A. Ramanathan} [Ann. Math. (2) 122, 27--40 (1985; Zbl 0601.14043)]).