  We single out the concept of concrete Hilbert module over a locally
$C^*$-algebra by means of locally bounded operators on certain strictly
inductive limits of Hilbert spaces. Using this concept, we construct an
operator model for all Hilbert locally $C^*$-modules and, as an application, we
obtain a direct construction of the exterior tensor product of Hilbert locally
$C^*$-modules. These are obtained as consequences of a general dilation theorem
for positive semidefinite kernels invariant under an action of a $*$-semigroup
with values locally bounded operators. As a by-product, we obtain two
Stinespring type theorems for completely positive maps on locally
$C^*$-algebras and with values locally bounded operators.
