  Let $\Gamma$ act on a countable set V with only finitely many orbits. Given a
$\Gamma$-invariant random environment for a Markov chain on V and a random
scenery, we exhibit, under certain conditions, an equivalent stationary measure
for the environment and scenery from the viewpoint of the random walker. Such
theorems have been very useful in investigations of percolation on
quasi-transitive graphs.
