Stable cohomology operation

Definition
A stable cohomology operation of type $$(\pi,G)$$ and of degree $$k$$ is defined as a set $$\{ \theta_n \}_{-\infty}^{\infty}$$ of cohomology operations $$\theta_n$$ of type $$(n,n+k,\pi,G)$$ such that $$\theta_{n-1}$$ is the cohomology suspension of $$\theta_n$$.

For a stable cohomology operation, all its constituent cohomology operations are group homomorphisms (this is not true for cohomology operations in isolation).