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For a finite group $G$, how is a rational $G$-spectrum $X$ detected by the geometric fixed point functor $\phi^H$ where we consider the conjugacy class of $H\leq G$? I tried finding a reference for ...

Let me first explain the statement of the question and then give some indication why the answer might be 'yes'. By a space I mean, say, a simplicial set and by rational I mean rational in the sense of ...