We present an axiomatic framework for Girard's Geometry of Interaction based on the notion
of linear combinatory algebra. We give a general construction on traced monoidal categories,
with certain additional structure, that is sufficient to capture the exponentials of Linear Logic,
which produces such algebras (and hence also ordinary combinatory algebras). We illustrate the
construction on six standard examples, representing both the ‘particle-style’ as
well as the ‘wave-style’ Geometry of Interaction.