  In the past decade, tremendous efforts have been made towards understanding
fermionic symmetry protected topological (FSPT) phases in interacting systems.
Nevertheless, for systems with continuum symmetry, e.g., electronic insulators,
it is still unclear how to construct an exactly solvable model with a finite
dimensional Hilbert space in general. In this paper, we give a lattice model
construction and classification for 2D interacting electronic insulators. Based
on the physical picture of $\mathrm{U(1)}_f$-charge decorations, we illustrate
the key idea by considering the well known 2D interacting topological
insulator. Then we generalize our construction to an arbitrary 2D interacting
electronic insulator with symmetry $G_f=\mathrm{U(1)}_f
\rtimes_{\rho_1,\omega_2} G$, where $\mathrm{U(1)}_f$ is the charge
conservation symmetry and $\rho_1, \omega_2$ are additional data which fully
characterize the group structure of $G_f$. Finally we study more examples,
including the full interacting classification of 2D crystalline topological
insulators.
