I am new to this subject; so please correct me if I will say something wrong or if you don't like my notation. In particular, I don't know whether it is reasonable to consider an infinite group $G$ (should it actually be a compact Lie group?) in my question. Also, for a group $G$ the corresponding stable homotopy category $SH\_G$ (should I use another notation?) also depends on the choice of a universe; does one get a canonical category taking a complete universe? 


As far as I understand equivariant stable homotopy theory, in $SH\_G$ one should take spectra $\Sigma\_G (G/H)\_+$ corresponding to all homogenious spaces $G/H$ to obtain a family of compact generators. Now, I want to know something on morphisms between these generators. In particular, is the group $Mor\_{SH\_G} (\Sigma\_G (G/H\_1)\_+, \Sigma\_G (G/H\_2)\_+[i])$ zero for any $i>0$ and all subgroups of $G$? This question seems to be related to [A heart for stable equivariant homotopy theory](https://mathoverflow.net/questions/36455/a-heart-for-stable-equivariant-homotopy-theory?rq=1)
Is there any text where I can find results of this sort? Possibly, one can say something about these morphism groups (say) using duality and apply some well-known results after that? 


Any hints would be very welcome!



Where can I find basic "computations" of equivariant stable homotopy groups?
Since Denis gave the right reference, namely <http://www.math.uchicago.edu/~may/BOOKS/equi.pdf>, I did not follow up and answer this question. We can work with any compact Lie group and any complete universe.
Working in the equivariant stable category always, with $S = S^0$,
$S^{-n}$ a negative sphere $G$-spectrum and $S^0$ and $S^n$
sphere spaces with trivial $G$-action, 
$$ \pi\_{-n}(S) = [S^{-n},S]\_G = [S,\Sigma^{\infty} S^n]\_G = [S^0, QS^n]\_G = 0 $$
where $Q^G$ is the functor $(colim\_V \Omega^V \Sigma^V(-))^G$, with $V$ running through
representations of $G$; $Q^G(X)$ is an $(n-1)$-connected $G$-space if $X$ is so. Replacing $S$ 
by $\Sigma^{\infty} G/H\_+$, the same argument works, using change of groups so that one is now looking at $[-,-]\_H$. More generally, the negative homotopy groups of the suspension $G$-spectrum of any $G$-space are zero, and the non-negative groups are calculated by the tom Dieck splitting theorem.


