  Study of stable isotopy classes of a finite collection of immersed circles
without triple or higher intersections on closed oriented surfaces is
considered as a planar analogue of virtual knot theory, a far reaching
generalisation of classical knot theory. Recent works have established
Alexander and Markov theorems in the planar setting. In the classical case, the
role of groups is played by twin groups, a class of right-angled Coxeter
groups. A new class of groups called virtual twin groups, that extends twin
groups in a natural way, plays the role of groups in the virtual case. The
virtual twin group $VT_n$ contains the pure virtual twin group $PVT_n$, a
planar analogue of the pure Artin braid group. In this paper, we prove that the
pure virtual twin group $PVT_n$ is an irreducible right-angled Artin group with
trivial center and give it's precise presentation. We show that $PVT_n$ has a
decomposition as an iterated semi-direct product of infinite rank free groups.
We give a complete description of the automorphism group of $PVT_n$ and
establish splitting of natural exact sequences of automorphism groups. As
applications, we show that $VT_n$ is residually finite and $PVT_n$ has the
$R_\infty$-property.
