  We use the conformal group to study non-local operators in conformal field
theories. A plane or a sphere (of any dimension) is mapped to itself by some
subgroup of the conformal group, hence operators confined to that submanifold
may be classified in representations of this subgroup. For local operators this
gives the usual definition of conformal dimension and spin, but some conformal
field theories contain interesting nonlocal operators, like Wilson or 't Hooft
loops. We apply those ideas to Wilson loops in four-dimensional CFTs and show
how they can be chosen to be in fixed representations of SL(2,R) x SO(3).
