Counting points of homogeneous varieties over finite fields

Let $X$ be an algebraic variety over a finite field ${\text{bF}}_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over ${\text{bF}}_{q^n}$ is a periodic polynomial function of $q^n$ with integer coefficients. Moreover, the shifted periodic polynomial function, where $q^n$ is formally replaced with $q^n+1$, is shown to have non-negative coefficients.