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. Our 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 process and flows on the non-commutative torus and the universal rotation algebra.