$\pi_*^C$ HZ: some elementary computations in equivariant (Bredon) homology and cohomology

In this talk I will present some elementary computations in
equivariant (Bredon) homology and cohomology.  First I will give a
brief introduction to equivariant homotopy theory and Bredon
(co)homology.  For the computations we will focus on the case of a
cyclic group G and constant coefficients Z.  We will compute the
equivariant (co)homology of the one point compactification of any
finite dimensional real G-representation.  Non-equivariantly these
spaces are just spheres, but their Bredon (co)homology groups will
usually have torsion.  The direct sum operation on representations
induces a product in the 'RO(G)-graded' theory.  Under this product we
will see that these computations can be unified in an elegant way.