  In the Isogeometric Analysis (IGA) framework, the computational domain has
very often a multipatch representation. The multipatch domain can be obtained
by a volume segmentation of a boundary represented domain, e.g., provided by a
Computer Aided Design (CAD) model. Typically, small gap and overlapping regions
can appear at the patch interfaces of such multipatch representations. In the
current work we consider multipatch representations having only small
overlapping regions between the patches.
  We develop a Discontinuous Galerkin (DG)- IGA method which can be immediately
applied to these representations. Our method appropriately connects the fluxes
of the one face of the overlapping region with the flux of the opposite face.
We provide a theoretical justification of our approach by splitting the whole
error into two components: the first is related to the incorrect representation
of the patches (consistency error) and the second to the approximation
properties of the IGA space. We show bounds for both components of the error.
We verify the theoretical error estimates in a series of numerical examples.
