  Profinite groups with a cyclotomic $p$-orientation are introduced and
studied. The special interest in this class of groups arises from the fact that
any absolute Galois group $G_{K}$ of a field $K$ is indeed a profinite group
with a cyclotomic $p$-orientation $\theta_{K,p}\colon
G_{K}\to\mathbb{Z}_p^\times$ which is even Bloch-Kato. The same is true for its
maximal pro-$p$ quotient $G_{K}(p)$ provided the field $K$ contains a primitive
$p^{th}$-root of unity. The class of cyclotomically $p$-oriented profinite
groups (resp. pro-$p$ groups) which are Bloch-Kato is closed with respect to
inverse limits, free product and certain fibre products. For profinite groups
with a cyclotomic $p$-orientation the classical Artin-Schreier theorem holds.
Moreover, Bloch-Kato pro-$p$ groups with a cyclotomic orientation satisfy a
strong form of Tits' alternative, and the elementary type conjecture formulated
by I. Efrat can be restated that the only finitely generated indecomposable
torsion free Bloch-Kato pro-$p$ groups with a cyclotomic orientation should be
Poincar\'e duality pro-$p$ groups of dimension less or equal to $2$.
