  We construct an exactly sovable commuting projector Hamiltonian for (2+1)D
bosonic topological insulator which is one of symmetry-protected topological
(SPT) phases protected by U(1) and time-reversal $\mathbb{Z}_2^T$ symmetry,
where the symmetry group is U(1)$\rtimes\mathbb{Z}_2^T$. The model construction
is based on the decorated domain-wall interpretation of the $E_{\infty}$-page
of a spectral sequence of a cobordism group that classifies the SPT phases in
question. We demonstrate nontriviality of the model by showing an emergence of
a Kramers doublet when the system is put on a semi-infinite cylinder
$(-\infty,0]\times S^1$ with an inserted $\pi$-flux. The surface anomaly
manifests itself as a non-onsite representation of the
U(1)$\rtimes\mathbb{Z}_2^T$ symmetry. Anomaly matching on a boundary is
discussed within a simple boundary theory.
