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Charles Rezk
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Since G is finite, there is no problem with just repeating the proof in the case G=e$G=e$, using Z$Z$-graded homotopy group functors on the orbit category. Take D^{\leq n}$D^{\leq n}$ to be the spectra whose homotopy groups \pi_q(X^H)$\pi_q(X^H)$ are zero for q>n$q>n$, and dually for D^{\geq n}$D^{\geq n}$. The intersection for n\leq 0$n\leq 0$ and n\geq 0$n\geq 0$ consists of the Eilenberg-MacLane G$G$-spectra K(M,0)$K(M,0)$ for Mackey functors M$M$. Peter

Peter May

Since G is finite, there is no problem with just repeating the proof in the case G=e, using Z-graded homotopy group functors on the orbit category. Take D^{\leq n} to be the spectra whose homotopy groups \pi_q(X^H) are zero for q>n, and dually for D^{\geq n}. The intersection for n\leq 0 and n\geq 0 consists of the Eilenberg-MacLane G-spectra K(M,0) for Mackey functors M. Peter May

Since G is finite, there is no problem with just repeating the proof in the case $G=e$, using $Z$-graded homotopy group functors on the orbit category. Take $D^{\leq n}$ to be the spectra whose homotopy groups $\pi_q(X^H)$ are zero for $q>n$, and dually for $D^{\geq n}$. The intersection for $n\leq 0$ and $n\geq 0$ consists of the Eilenberg-MacLane $G$-spectra $K(M,0)$ for Mackey functors $M$.

Peter May

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Peter May
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Since G is finite, there is no problem with just repeating the proof in the case G=e, using Z-graded homotopy group functors on the orbit category. Take D^{\leq n} to be the spectra whose homotopy groups \pi_q(X^H) are zero for q>n, and dually for D^{\geq n}. The intersection for n\leq 0 and n\geq 0 consists of the Eilenberg-MacLane G-spectra K(M,0) for Mackey functors M. Peter May