Partial Wave Analysis of $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$

BES data on $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$ are presented. The $K^*\bar K^*$ contribution peaks strongly near threshold. It is fitted with a broad $0^{-+}$ resonance with mass $M = 1800 \pm 100$ MeV, width $\Gamma = 500 \pm 200$ MeV. A broad $2^{++}$ resonance peaking at 2020 MeV is also required with width $\sim 500$ MeV. There is further evidence for a $2^{-+}$ component peaking at 2.55 GeV. The non-$K^*\bar K^*$ contribution is close to phase space; it peaks at 2.6 GeV and is very different from $K^{*}\bar{K^{*}}$.