  In this paper we continue the study initiated in [FGN] concerning the
obstacle problem for a class of parabolic non-divergence operators structured
on a set of vector fields X = {X_1,...,X_q} in R^n with C^1-coefficients
satisfying H\"ormander's finite rank condition, i.e., the rank of
Lie{X_1,...,X_q} equals n at every point in R^n. In [FGN] we proved, under
appropriate assumptions on the operator and the obstacle, the existence and
uniqueness of strong solutions to a general obstacle problem. The main result
of this paper is that we establish further regularity, in the interior as well
as at the initial state, of strong solutions. Compared to [FGN] we in this
paper assume, in addition, that there exists a homogeneous Lie group G = (R^n,
\circ, \delta_\lambda) such that {X_1,...,X_q} are left translation invariant
on G and such that {X_1,...,X_q} are \delta_\lambda-homogeneous of degree one.

Analysis of PDEs