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

Bordism-finiteness and semi-simple group actions