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Let $G$ be a finite group and $H$ be a subgroup of $G$ . Let us denote $X= G/H \ast G/H \ast \cdots \ast G/H $($k$ times).Where $\ast$ denotes the topological join operation. My question are as follows:

Question 1: What should be a $G$-CW complex structure of $X$?

Edit Question 2 : How to calculate the integer graded Bredon cohomology of $X$ with a constant coefficient system?

Any hint or references will be appreciated.

Thank you.

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    $\begingroup$ The join of discrete sets is naturally a simplicial complex, hence a CW complex. The $G$-action on $G/H$ induces a diagonal $G$-action on $X$, under which it becomes a $G$-CW complex. $\endgroup$
    – Mark Grant
    Commented Aug 24, 2015 at 15:14
  • $\begingroup$ @MarkGrant: I understand your point. But I want to calculate the integer graded Bredon cohomology of $X$ with a constant coefficient system. $\endgroup$
    – Surojit
    Commented Aug 24, 2015 at 15:21
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    $\begingroup$ @Surojit so you complain that Mark Grant didn't answer a question you didn't pose? I think Mark's answer does answer your question. Maybe you should open a new thread if you have a new question. $\endgroup$
    – Fernando Muro
    Commented Aug 24, 2015 at 15:27
  • $\begingroup$ @FernandoMuro: Sorry Sir. I don't want to mean this. $\endgroup$
    – Surojit
    Commented Aug 24, 2015 at 15:30

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