The ordinary cohomology transfer associated to the orbit space projection of a finite group action need not commute with stable cohomology operations. In particular, if an even group acts on a space, the resulting transfer
τ
\tau
will not generally commute with the Steenrod squares,
S
q
i
{\text {S}}{{\text {q}}^i}
. This paper contains a formula for the deviation from commutativity
(
S
q
i
τ
−
τ
S
q
i
)
x
({\text {S}}{{\text {q}}^i}\tau - \tau {\text {S}}{{\text {q}}^i})x
in the case of an involution. The formula involves the restriction of
x
x
to the cohomology of the fixed point set, as well as certain naturally occurring characteristic classes.