Group Actions and the Topology of Nonnegatively Curved 4-manifolds ?

We consider nonnegatively curved 4-manifolds that admit effective isometric actions by nite groups and from that draw topological conclusions about the manifold. Our rst theorem shows that if the man-ifolds admits an isometric Zp Zp for p large enough that the manifold has Euler characteristic less than or equal to ve. Our second theorem requires no hypothesis on the structure of the group other then that it be large but it does require the manifold to be ?pinched, in which case we can then again conclude that the Euler characteristic is less than or equal to ve.