0MYC Theorem 3.14. The weight complex functor induces an equivalence t:DTMG(k,ℚ)→Dperfℤ(SW⋉ℚ[π0(G)]).t:\operatorname{DTM}_{G}(k,\mathbb{Q})\to\operatorname{D}^{\mathbb{Z}}_{\operatorname{perf}}(S^{W}\ltimes\mathbb{Q}[\pi_{0}(G)]).