Author’s summary: Let \(\Gamma\) be a group, \(F\Gamma\) the free \(\mathbb{C}\)-module on the set of finite order elements in \(\Gamma\), with \(\Gamma\) acting by conjugation, and \(\mathbb{Z}_\Gamma\) the ring extension of \(\mathbb{Z}\) by \(\{\tfrac 1ne^{2\pi i/n}\mid \exists\gamma\in\Gamma\) of order \(n\}\). For a ring \(R\) with \(\mathbb{Z}_\Gamma\subseteq R\subseteq\mathbb{C}\), we build an injective assembly map \(\alpha^{\Gamma,R}_*\colon H_*(\Gamma;F\Gamma)\hookrightarrow K^{\text{alg}}_*(R\Gamma)\otimes_\mathbb{Z}\mathbb{C}\), detected by the Dennis trace map. This is proved by establishing a ‘delocalization property’ for the assembly map \(\theta^\Gamma_*\) in the Hochschild homology, namely providing a gluing of simpler assembly maps (i.e., ‘localized at the identity of \(\Gamma\)’) to build \(\theta^\Gamma_*\), and by ‘delocalizing’ a known assembly map in \(K\)-theory to define \(\alpha^{\Gamma,R}_*\). We also prove the delocalization property in cyclic homology and in related theories.