  This paper proposes a connection between algebraic K-theory and foam
cobordisms, where foams are stratified manifolds with singularities of a
prescribed form. We consider $n$-dimensional foams equipped with a flat bundle
of finitely-generated projective $R$-modules over each facet of the foam,
together with gluing conditions along the subfoam of singular points. In a
suitable sense which will become clear, a vertex (or the smallest stratum) of
an $n$-dimensional foam replaces an $(n+1)$-simplex with a total ordering of
vertices. We show that the first K-theory group of a ring $R$ can be identified
with the cobordism group of decorated 1-foams embedded in the plane. A similar
relation between the $n$-th algebraic K-theory group of a ring $R$ and the
cobordism group of decorated $n$-foams embedded in $\mathbb{R}^{n+1}$ is
expected for $n>1$. An analogous correspondence is proposed for arbitrary exact
categories. Modifying the embedding and other conditions on the foams may lead
to new flavors of K-theory groups.
