Why orientation-preserving self-homeomorphism of $\mathbb{C}P^n$ when $n$ is odd must have fixed points?

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I have the following question: Suppose the map $g: \mathbb{C}P^n \rightarrow \mathbb{C}P^n$ is a orientation-preserving homeomorphism when $n$ is odd, then how to prove that $g$ must have fixed points? Thanks!