I am trying to understand basic notions from Hill-Hopkins-Ravenel paper: https://arxiv.org/abs/0908.3724

In the Example 3.10 we are considering equviariant cellular chain complex for $n$-dimensional representation $V$ of a group $G$ $$ \ldots\to C^{cell}_n(S^V;\underline{\mathbb{Z}})\to C^{cell}_{n-1}(S^V;\underline{\mathbb{Z}})\to\ldots\to C^{cell}_0(S^V;\underline{\mathbb{Z}}). $$ The underlying homology groups are those of the sphere $S^V$ - in particular kernel of the map $C^{cell}_n(S^V;\underline{\mathbb{Z}})\to C^{cell}_{n-1}(S^V;\underline{\mathbb{Z}})$ is isomorphic as a $G$-module to nonequivariant homology of $S^V$ (denoted as $H^u_n(S^V;\mathbb{Z}))$.

Now if $V$ is oriented (so I suppose this means that group action preserves orientation), then $G$ acts trivially on $C^{cell}_n(S^V;\underline{\mathbb{Z}})$ (? I am not sure about this statement) and we obtain that $H^G_*(S^V;\mathbb{Z})\cong H^u_n(S^V;\mathbb{Z}).$

**Question:** Why if $V$ is oriented we obtain such result?

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