  Let G be a Lie group equipped with a set of left invariant vector fields.
These vector fields generate a function \xi on Wiener space into G via the
stochastic version of Cartan's rolling map. It is shown here that, for any
smooth function f with compact support, f(\xi) is Malliavin differentiable to
all orders and these derivatives belong to L^p(\mu) for all p>1, where \mu is
Wiener measure.
