  Given an action $\alpha$ of a discrete group $G$ on a unital C*-algebra $A$,
we introduce a natural concept of $\alpha$-negative definiteness for functions
from $G$ to $A$, and examine some of the first consequences of such a notion.
In particular, we prove analogs of theorems due to Delorme-Guichardet and
Schoenberg in the classical case where $A$ is trivial. We also give a
characterization of the Haagerup property for the action $\alpha$ when $G$ is
countable.
