Homomorphisms of two-dimensional linear groups over a ring of stable range one

Let R be a commutative domain of stable range 1 with 2 a unit. This paper describes the homomorphisms between SL(2,R) and GL(2,K) where K is an algebraically closed field. It is shown that evey non-trivial homomorphism can be decomposed uniquely as a product of an inner automorphism and a homomorphism induced by a morphism between R and K. Furthermore, the homomorphisms between GL(2,R) and GL(2,K) are found of either the extensions of homomorphisms from SL(2,R) to GL(2,K) or the products of inner automorphisms with certain group homomorphisms from GL(2,R) to K.