\title{Multiplicative equivariant formal group laws.}
\author{J.P.C.Greenlees}
\address{School of Mathematics and Statistics, Hicks Building,
Sheffield S3 7RH. UK.}
\email{j.greenlees@sheffield.ac.uk}
\begin{abstract}
The notion of an $A$-equivariant formal group law
for a compact abelian Lie group $A$ was introduced to study complex oriented
$A$-equivariant formal group laws, but has some intrinsic algebraic
interest. The theorem that the coefficient ring of equivariant
complex bordism is the universal ring for equivariant formal group laws
establishes that the definition is the correct one.
We shall be concerned here with a very special class of equivariant
formal group laws: the multiplicative ones,
which appear to play a privileged role amongst all equivariant formal group
laws. However our principal motivation for considering this case is
its importance in understanding equivariant
K-theories, and its close relationship to representation theory.
The universal ring for multiplicative equivariant formal group laws
is shown to be closely related to the Rees ring of
the representation ring at the augmentation ideal, but only equal to
it if the group is topologically cyclic.
\end{abstract}