A fixed point index for equivariant maps

Abstract

The purpose of the paper is to define a fixed point index
for equivariant maps of $G$-ENR's
and to state and prove some of its properties, such as
the compactly fixed $G$-homotopy property, the Lefschetz property,
its converse, and the retraction property. At the end,
some examples are given of equivariant self-maps which
have a nonzero index (hence cannot be deformed equivariantly to
be fixed point free) but have a zero $G$-Nielsen invariant.