Given a principal G bundle E® B (where G is a compact Lie group and E and B are closed manifolds), one would like to know if the isometry group of B can be mada to act on E via bundle maps. This question was asked in the 60's by Palais and Stewart and they answered it when G is a torus. There were various suibsequent proofs of this result. We give another proof based on Yang-Mills theory. We also formulate the question for the case of G being a general compact Lie group and discuss related issues.