Positive Scalar Curvature with Symmetry

We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension2 surgery technique which removes singular strata from fixed point free S-manifolds while preserving equivariant positive scalar curvature. These results are applied to derive the following generalization of a result of Gromov and Lawson: Each closed fixed point free S-manifold of dimension at least 6 whose isotropy groups have odd order and whose union of maximal orbits is simply connected and not spin carries an S-invariant metric of positive scalar curvature.