  We introduce some braided varieties -- braided orbits -- by considering
quotients of the so-called Reflection Equation Algebras associated with Hecke
symmetries (i.e. special type solutions of the quantum Yang-Baxter equation).
Such a braided variety is called regular if there exists a projective module on
it, which is a counterpart of the cotangent bundle on a generic orbit O in
gl(m)* in the framework of the Serre approach. We give a criterium of
regularity of a braided orbit in terms of roots of the Cayley-Hamilton identity
valid for the generating matrix of the Reflection Equation Algebra in question.
By specializing our general construction we get super-orbits in gl(m|n)* and a
criterium of their regularity.
