  We investigate Cohen-Macaulay representations of quotient singularities
$R:=l[[x_1,\cdots,x_d]]^G$ where $l$ is a field and $G$ is a finite group
acting on $l[[x_1,\cdots,x_d]]$ as a ring, not necessarily as an $l$-algebra,
with $|G|$ not divided by ${\rm char}\, l$. In fact, if we put $k:=l^G$, then
we may assume that $G$ is a subgroup of $GL_d(l)\rtimes{\rm Gal}(l/k)$. We show
that $R$ has a generator giving an NCCR and therefore when $d=2$, it is of
finite Cohen-Macaulay type. Additionally, we completely describe its
Auslander-Reiten quiver, which is often non-simply laced, as a quotient of a
certain quiver. Moreover, we also prove that two-dimensional rings of finite
Cohen-Macaulay type of equicharacteristic zero are precisely quotient
singularities of this form, which generalizes Esnault and Auslander's result.
Combining these results, we prove that the quivers that may arise as the
Auslander-Reiten quiver of a two-dimensional Gorenstein ring of finite
Cohen-Macaulay type of equicharacteristic zero are either doubles of extended
Dynkin diagrams or ones having loops. To accomplish these, we establish two
results which are of independent interest. First, we prove the existence of
$(d-1)$-almost split sequences for arbitrary Cohen-Macaulay normal rings having
NCCR which are not necessarily isolated singularities. Second, we make it
possible to determine simple modules over skew group algebras by relating them
to those over certain group algebras.
