  We have investigated exchange bias effects in bilayers composed by the
antiferromagnetic o-YMnO$_3$ and ferromagnetic Co thin film by means of SQUID
magnetometry, magnetoresistance, anisotropic magnetoresistance and planar Hall
effect. The magnetization and magnetotransport properties show pronounced
asymmetries in the field and magnetization axes of the field hysteresis loops.
Both exchange bias parameters, the exchange bias field $H_{E}(T)$ as well as
the magnetization shift $M_E(T)$, vanish around the N\'eel temperature $T_N
\simeq 45$ K. We show that the magnetization shift $M_E(T)$ is also measured by
a shift in the anisotropic magnetoresistance and planar Hall resistance having
those a similar temperature dependence as the one obtained from magnetization
measurements. Because the o-YMnO$_3$ film is highly insulating, our results
demonstrate that the $M_E(T)$ shift originates at the interface within the
ferromagnetic Co layer. To show that the main results obtained are general and
not because of some special characteristics of the o-YMO$_3$ layer, similar
measurements were done in Co/CoO micro-wires. The transport and magnetization
characterization of the micro-wires supports the main conclusion that these
effects are related to the response of the ferromagnetic Co layer at the
interface.
