\author{Michael Cole}
\address{Department of Mathematics, Hofstra University, Hempstead, NY  11549, 
USA.}
\author{J.P.C.Greenlees}
\address{School of Mathematics and Statistics, Hicks Building, 
Sheffield S3 7RH. UK.}
\author{I.Kriz}
\address{Department of Mathematics, University of Michigan, Ann Arbor, 
MI 48109-1003}
Title: The universality of equivariant complex cobordism

Abstract:
We show that if $A$ is an abelian compact Lie group, all $A$-equivariant 
complex vector bundles are orientable over a complex orientable equivariant 
cohomology theory. In the process,  we calculate the complex orientable
homology and cohomology of all complex Grassmannians.