  We associate to a full flag $\mathcal{F}$ in an $n$-dimensional variety $X$
over a field $k$, a "symbol map" $\mu_{\mathcal{F}}:K(F_X) \to \Sigma^n K(k)$.
Here, $F_X$ is the field of rational functions on $X$, and $K(\cdot)$ is the
$K$-theory spectrum. We prove a "reciprocity law" for these symbols: Given a
partial flag, the sum of all symbols of full flags refining it is $0$.
Examining this result on the level of $K$-groups, we re-obtain various
"reciprocity laws". Namely, when $X$ is a smooth complete curve, we obtain
degree of a principal divisor is zero, Weil reciprocity, Residue theorem,
Contou-Carr\`{e}re reciprocity. When $X$ is higher-dimensional, we obtain
Parshin reciprocity.
