  We classify finite groups acting by birational transformations of a
non-trivial Severi--Brauer surface over a field of characteristc zero that are
not conjugate to subgroups of the automorphism group. Also, we show that the
automorphism group of a smooth cubic surface over a field $K$ of characteristic
zero that has no $K$-points is abelian, and find a sharp bound for the Jordan
constants of birational automorphism groups of such cubic surfaces.
