  Soergel bimodules and their Hochschild homology are known to be important in
the context of link homology. In this article we observe that Soergel bimodules
may be naturally identified as the cohomology of well-defined objects in the
category of spectra. This allows us to define forms of Soergel bimodules over
the integers after inverting 2, indexed by elements in Braid groups associated
to compact Lie groups of adjoint type. Reducing the Soergel bimodules modulo an
odd prime, we endow the bimodules with an action of the reduced Steenrod
algebra. This action extends to an action of the reduced Steenrod algebra on
the Hochschild homology of Soergel bimodules over the primary field F_p for odd
primes p. In the special case of the n-stranded Braid group, our results allow
us to define the triply graded link homology over any ring where 2 is
invertible, and deduce that the reduced Steenrod algebra acts on triply graded
link homology over the field F_p for odd primes p.
