  We describe space-time using split octonions over the reals and use their
group of automorphisms, the non-compact form of Cartan's exceptional Lie group
G2, as the main geometrical group of the model. Connections of the G2-rotations
of octonionic 8D space with the conformal transformations in 4D Minkowski
space-time are studied. It is shown that the dimensional constant needed in
these analysis naturally gives the observed value of the cosmological constant.
