Bordism of two commuting involutions

In this paper we obtain conditions for a Whitney sum of three vector bundles over a closed manifold, epsilon(1) + epsilon(2) + epsilon(3) --> F, to be the fixed data of a (Z(2))(2)-action; these conditions yield the fact that if (epsilon(1) + R) + epsilon(2) + epsilon(3) --> F is the fixed data of a (Z(2))(2)-action, where R --> F is the trivial one dimensional bundle, then the same is true for epsilon(1) + epsilon(2) + epsilon(3) --> F. The results obtained, together with techniques previously developed, are used to obtain, up to bordism, all possible (Z(2))(2)-actions fixing the disjoint union of an even projective space and a point.