Computing Equivariant Homotopy with a Splitting Method

We develop a new method in the computation of equivariant homotopy, which is based on the splitting of cofiber sequences associated to universal spaces in the category of equivariant spectra. With this method, the homotopy of $G$-spectra can be decomposed into the homotopy of some spectra acted on by $p$-subgroups of $G$. In particular, we use this method to compute the homotopy of $H\underline{\mathbb{Z}}$ for $G=D_{2p}$ and $A_5$.