  A family of TQFTs parametrised by G-crossed braided spherical fusion
categories has been defined recently as a state sum model and as a Hamiltonian
lattice model. Concrete calculations of the resulting manifold invariants are
scarce because of the combinatorial complexity of triangulations, if nothing
else. Handle decompositions, and in particular Kirby diagrams are known to
offer an economic and intuitive description of 4-manifolds. We show that if
3-handles are added to the picture, the state sum model can be conveniently
redefined by translating Kirby diagrams into the graphical calculus of a
G-crossed braided spherical fusion category.
  This reformulation is very efficient for explicit calculations, and the
manifold invariant is calculated for several examples. It is also shown that in
most cases, the invariant is multiplicative under connected sum, which implies
that it does not detect exotic smooth structures.
