  We construct the Hubble diagram (HD) of Gamma-Ray Bursts (GRBs) with
redshifts reaching up to $z \sim 6$, by using five luminosity vs. luminosity
indicator relations calibrated with the Cardassian cosmology. This model has a
major interesting feature: despite of being matter-dominated and flat, it can
explain the present accelerate expansion of the universe. This is the first
study of this class of models using high redshift GRBs. We have performed a
$\chi$-square statistical analysis of the GRBs calibrated with the Cardassian
model, and also combined them with both the current Cosmic Microwave Background
and Baryonic Acoustic Oscillation data. Our results show consistency between
the current observational data and the model predictions. In particular, the
best-fit parameters obtained from the $\chi^2$-analysis are in agreement with
those obtained from the Concordance Cosmology ($\Lambda$-CDM). We determine the
redshift at which the universe would start to follow the Cardassian expansion,
i. e., \zc, and both the redshift at which the universe had started to
accelerate, i. e., \zac, and the age-redshift relation $H_0t_0$. Our results
also show that the universe, from the point of view of GRBs, had undergo a
transition to acceleration at a redshift $z \approx 0.2-0.7$, which agrees with
the SNIa results. Hence, after confronting the Cardassian scenario with the
GRBs HD and proving its consistency with it, we conclude that GRBs should
indeed be considered a complementary tool to several other astronomical
observations for studies of high accuracy in cosmology.
