Our aim is to combine the geometric approach of Conner and Floyd (see [9], [lo], [ll], [13]) and the K-theory approach which is contained in papers by Atiyah, Bott, Segal and Singer ([ 11, [2], [3]). For simplicity of exposition we restrict to unitary cobordism. We develop cobordism analogue of K-theory integrality theorems and show their relation to the results of Conner and Floyd. We get a systematic and conceptual understanding of various results about (unitary) G-manifolds. We now describe our techniques and results. Tn Section 1 we define equivariant cobordism U,*(X) along the lines of G. W. Whitehead [23], using all representations of the compact Lie group G for suspending. We construct a natural transformation a: U,*(X)-+ U*(EG x,X) LEMMA 1.1. Any two isomorphisms f, g : V-+ W of complex G-modules are homotopic as G-isomorphisms.
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