  This paper is centered around the classical problem of extracting properties
of a finite group $G$ from the ring isomorphism class of its integral group
ring $\mathbb{Z} G$. This problem is considered via describing the unit group
$\mathcal{U}( \mathbb{Z} G)$ generically for a finite group. Since the $90's$
several well known generic constructions of units are known to generate a
subgroup of finite index in $\mathcal{U}(\mathbb{Z } G)$ if $\mathbb{Q} G$ does
not have so-called exceptional simple epimorphic images, e.g. $M_2
(\mathbb{Q})$. However it remained a major open problem to find a {\it generic}
construction under the presence of the latter type of simple images. In this
article we obtain such generic construction of units. Moreover, this new
construction also exhibits new properties, such as providing generically free
subgroups of large rank. As an application we answer positively for several
classes of groups recent conjectures on the rank and the periodic elements of
the abelianisation $\mathcal{U}(\mathbb{Z} G)^{ab}$. To obtain all this, we
investigate the group ring $R \Gamma$ of an extension $\Gamma$ of some normal
subgroup $N$ by a group $G$, over a domain $R$. More precisely, we obtain a
direct sum decomposition of the (twisted) group algebra of $\Gamma$ over the
fraction field $F$ of $R$ in terms of various twisted group rings of $G$ over
finite extensions of $F$. Furthermore, concrete information on the kernel and
cokernel of the associated projections is obtained. Along the way we also
launch the investigations of the unit group of twisted group rings and of
$\mathcal{U}( R\Gamma)$ via twisted group rings.
