Title: Equivariant homotopy theory for pro--spectra

Author:  Halvard Fausk 

fausk@math.uio.no

Abstract.
We extend the theory of equivariant orthogonal spectra from finite groups to profinite 
groups, and more generally from compact Lie groups to compact Hausdorff groups.
The $G-$homotopy theory  is   ``pieced  together'' from the $G/U-$homotopy theories 
for suitable quotient groups $G/U$ of $G$;  a motivation is the way
continuous group cohomology of a profinite group is built out of the cohomology
of its finite quotient groups.  In this category Postnikov towers are studied  from a
general perspective. We introduce pro$-G-$spectra and construct various model structures 
on them. A key property of the model structures is that pro-spectra are
weakly equivalent to their  Postnikov towers.  We give a careful discussion of 
two version of a model structure with ``underlying weak equivalences''. 
One of the versions only make sense for pro$-$spectra. In the end we  use the theory to
study  homotopy fixed points of pro$-G-$spectra.