  We have studied the consequences of breaking the CPT symmetry in the neutrino
sector, using the expected high-energy neutrino flux from distant cosmological
sources such as active galaxies. For this purpose we have assumed three
different hypotheses for the neutrino production model, characterised by the
flavour fluxes at production \phi_e^0:\phi_\mu^0:\phi_\tau^0 = 1:2:0, 0:1:0,
and 1:0:0, and studied the theoretical and experimental expectations for the
muon-neutrino flux at Earth, \phi_\mu, and for the flavour ratios at Earth, R =
\phi_\mu/\phi_e and S = \phi_\tau/\phi_\mu. CPT violation (CPTV) has been
implemented by adding an energy-independent term to the standard neutrino
oscillation Hamiltonian. This introduces three new mixing angles, two new
eigenvalues and three new phases, all of which have currently unknown values.
We have varied the new mixing angles and eigenvalues within certain bounds,
together with the parameters associated to pure standard oscillations. Our
results indicate that, for the models 1:2:0 and 0:1:0, it might possible to
find large deviations for \phi_\mu, R, and S between the cases without and with
CPTV, provided the CPTV eigenvalues lie within 10^{-29}-10^{-27} GeV, or above.
Moreover, if CPTV exists, there are certain values of R and S that can be
accounted for by up to three production models. If no CPTV were observed, we
could set limits on the CPTV eigenvalues of the same order. Detection prospects
calculated using IceCube suggest that for the models 1:2:0 and 0:1:0, the
modifications due to CPTV are larger and more clearly separable from the
standard-oscillations predictions. We conclude that IceCube is potentially able
to detect CPTV but that, depending on the values of the CPTV parameters, there
could be a mis-determination of the neutrino production model.
