Connor and Floyd have observed that a free action of a finite group G G on a compact manifold M M preserving a stable almost complex structure produces a stably almost complex quotient manifold M / G M/G . Hence, the bordism group of such actions, U ∗ G , free U_ \ast ^{G,{\text {free}}} , is just U ∗ ( B G ) {U_ \ast }(BG) . If G G is not finite or abelian, but an arbitrary compact Lie group, the tangent bundle along the fibres gives trouble. Nevertheless, it is shown that if H ∗ ( B G ) {H^ \ast }(BG) is torsion free then U ∗ G , free ≈ U ∗ ( B G ) U_ \ast ^{G,{\text {free}}} \approx {U_ \ast }(BG) .