  Let $G$ be a finite group. We re-analyze the splitting of rational
$G$-spectra, which is discussed in Barne's thesis and traces back to Greenlees
and May. We will study how the splitting behaves under a localization which is
weaker than rationalization and discuss its application in computing
equivariant cohomology of $G$-spectra. In particular, we will explicitly
compute $\pi_\bigstar(H\underline{\mathbb{Z}})$ and $\pi_\bigstar(HA_G)$ for
the dihedral group $G=D_{2p}$. The additive structures and partial
multiplicative structures are already computed by Kriz, Lu, and Zou. Our new
method will provide a systematic way to compute them as $RO(D_{2p})$-graded
rings.
