  In this paper we address the celebrated Albert problem for exceptional Jordan
algebras (i.e. Albert algebras): Does every Albert division algebra contain a
cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a
field $k$ of arbitrary characteristic, there is a suitable isotope that
contains a cubic cyclic subfield. It follows from this that for any Albert
division algebra $A$ over a field $k$, the structure group $\text{\bf Str}(A)$
always contains a subgroup of type $^3D_4$ defined over $k$.
