  Let K be any field, and let G be a semisimple group over K. Suppose the
characteristic of K is positive and is very good for G. We describe all group
scheme homomorphisms phi:SL(2) --> G whose image is geometrically G-completely
reducible -- or G-cr -- in the sense of Serre; the description resembles that
of irreducible modules given by Steinberg's tensor product theorem. In case K
is algebraically closed and G is simple, the result proved here was previously
obtained by Liebeck and Seitz using different methods. A recent result shows
the Lie algebra of the image of phi to be geometrically G-cr; this plays an
important role in our proof.
