Quasi-invariance for the pinned Brownian motion on a Lie group

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by finite energy paths. The main technique we use is the time reversal. This approach is different from what B. Driver used to prove quasi-invariance for the pinned Brownian motion on a compact Riemannian manifold.