  We consider a transmission problem consisting of a singularly perturbed
reaction diffusion equation on a bounded domain and the Laplacian in the
exterior, connected through standard transmission conditions. We establish a
DPG scheme coupled with Galerkin boundary elements for its discretization, and
prove its robustness for the field variables in so-called balanced norms. Our
coupling scheme is the one from [F\"uhrer, Heuer, Karkulik: On the coupling of
DPG and BEM, arXiv:1508.00630], adapted to the singularly perturbed case by
using the scheme from [Heuer, Karkulik: A robust DPG method for singularly
perturbed reaction diffusion problems, arXiv:1509.07560]. Essential feature of
our method is that optimal test functions have to be computed only locally. We
report on various numerical experiments in two dimensions.
