  We devise a unitary transformation that replaces the fermionic degrees of
freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting
theory is local and gauge invariant, with the same symmetry group. The method
works in any spatial dimensions and can be directly applied, among others, to
the gauge groups $G=U(N)$ and $SU(2N)$, where $N\in\mathbb{N}$. For $SU(2N+1)$
one can also carry out the transformation after introducing an extra idle
$\mathbb{Z}_2$ gauge field, so that the resulting symmetry group trivially
contains $\mathbb{Z}_2$ as a normal subgroup. Those results have implications
in the field of quantum simulations of high-energy physics models.
