  This note explores the interaction between cohomology operations in a
generalized cohomology theory and a string topology loop coproduct dual to the
Chas--Sullivan loop product. More precisely, we ask for a description for the
failure of a given operation to commute with the loop coproduct, and will
obtain a satisfactory answer in the case where the operation preserves both
sums and products. Examples of such operations include the total Steenrod
square in ordinary mod 2 cohomology and the Adams operations in K-theory.
