H-Space structures on spaces of metrics of positive scalar curvature

We construct and study an $H$-space multiplication on ${\mathcal{R}}^{+}(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for the action of the diffeomorphism group on ${\mathcal{R}}^{+}(M)$ via pullback. We also compare this to other known multiplicative structures on ${\mathcal{R}}^{+}(M)$.