  We design an adaptive unfitted finite element method on the Cartesian mesh
with hanging nodes. We derive an hp-reliable and efficient residual type a
posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain
inverse estimate which allows us to prove the stability of the finite element
method under practical interface resolving mesh conditions and also prove the
lower bound of the hp a posteriori error estimate. Numerical examples are
included.
