The efforts in the study of abstract homomorphisms between the groups of rational points of algebraic groups are aimed at proving that under certain conditions any group homomorphism ยต G k โ G k where G and G are algebraic groups over (infinite) fields k and k , respectively, can be obtained from a field homomorphism k โ k and a k -rational homomorphism k G โ G , where k G is obtained by the change of scalars from k to k (such homomorphisms are called standard). In their fundamental paper [BoT], Borel and Tits showed, in particular, that if G and G are absolutely simple, G is k-isotropic, and ยต has a Zariski dense image, then any homomorphism ยต is (basically) standard [BoT, 8.1]. In fact, the main result of [BoT] is more general and describes abstract homomorphisms when only G is assumed to be absolutely simple (and k-isotopic) while G is allowed to be an arbitrary reductive group, but its statement is more technical (cf. [BoT, 8.16]). In the same paper ([BoT, 8.18]) Borel and Tits pointed out that dropping the assumption that G is reductive opens a way to the existence of essentially new homomorphisms. Namely, given a field extension K/k and a derivation ฮด k โ K, for any algebraic group G 374