  It is shown how to construct *-homomorphic quantum stochastic Feller cocycles
for certain unbounded generators, and so obtain dilations of strongly
continuous quantum dynamical semigroups on C* algebras; this generalises the
construction of a classical Feller process and semigroup from a given
generator. The construction is possible provided the generator satisfies an
invariance property for some dense subalgebra A_0 of the C* algebra A and obeys
the necessary structure relations; the iterates of the generator, when applied
to a generating set for A_0, must satisfy a growth condition. Furthermore, it
is assumed that either the subalgebra A_0 is generated by isometries and A is
universal, or A_0 contains its square roots. These conditions are verified in
four cases: classical random walks on discrete groups, Rebolledo's symmetric
quantum exclusion processes and flows on the non-commutative torus and the
universal rotation algebra.
