  This paper contributes to the characterization of a certain class of
commutative Hopf algebroids. It is shown that a commutative flat Hopf algebroid
with a non zero base ring and a nonempty character groupoid is geometrically
transitive if and only if any base change morphism is a weak equivalence (in
particular, if any extension of the base ring is Landweber exact), if and only
if any trivial bundle is a principal bi-bundle, and if and only if any two
objects are fpqc locally isomorphic. As a consequence, any two isotropy Hopf
algebras of a geometrically transitive Hopf algebroid (as above) are weakly
equivalent. Furthermore, the character groupoid is transitive and any two
isotropy Hopf algebras are conjugated. Several other characterizations of these
Hopf algebroids in relation to transitive groupoids are also given.
