  We propose the analogues of boundary layer potentials for the sub-Laplacian
on homogeneous Carnot groups/stratified Lie groups and prove continuity results
for them. In particular, we show continuity of the single layer potential and
establish the Plemelj type jump relations for the double layer potential. We
prove sub-Laplacian adapted versions of the Stokes theorem as well as of
Green's first and second formulae on homogeneous Carnot groups. Several
applications to boundary value problems are given. As another consequence, we
derive formulae for traces of the Newton potential for the sub-Laplacian to
piecewise smooth surfaces. Using this we construct and study a nonlocal
boundary value problem for the sub-Laplacian extending to the setting of the
homogeneous Carnot groups M. Kac's "principle of not feeling the boundary". We
also obtain similar results for higher powers of the sub-Laplacian. Finally, as
another application, we prove refined versions of Hardy's inequality and of the
uncertainty principle.
