Borel-Tits theorem

Statement
Let $$G$$ be a simple algebraic group over an algebraically closed field $$K$$, and $$H$$ be a simple algebraic group over an algebraically closed field $$L$$. Let $$s$$ be an isomorphism of groups between $$G$$ and $$H$$ (viz, only an isomorphism of the pure group structure). Then $$s$$ can be decomposed into a transfer of structures induced by an isomorphism between $$K$$ and $$L$$, followed by a quasi-rational function relative to $$L$$.