  We give bordism-finiteness results for manifolds with semi-simple group
action. Consider the class of oriented manifolds which admit a circle action
with isolated fixed points such that the action extends to an $S^3$-action with
fixed point. We exhibit various subclasses, characterized by an upper bound for
the Euler characteristic and properties of the first Pontrjagin class, which
contain only finitely many oriented bordism types in any given dimension. Also
we show finiteness results for homotopy complex projective spaces and complete
intersections with $S^3$-action as above.
