  Trojans are circumstellar bodies that reside in characteristic 1:1 orbital
resonances with planets. While all the trojans in our Solar System are small (<
~100 km), stable planet-size trojans may exist in extrasolar planetary systems,
and the Kepler telescope constitutes a formidable tool to search for them. Here
we report on a systematic search for extrasolar trojan companions to 2244 known
Kepler Objects of Interest (KOIs), with epicyclic orbital characteristics
similar to those of the Jovian trojan families. No convincing trojan candidates
are found, despite a typical sensitivity down to Earth-size objects. This fact
can however not be used to stringently exclude the existence of trojans in this
size range, since stable trojans need not necessarily share the same orbital
plane as the planet, and thus may not transit. Following this reasoning, we
note that if Earth-sized trojans exist at all, they are almost certainly both
present and in principle detectable in the full set of Kepler data, although a
very substantial computational effort would be required to detect them. On the
same token, we also note that some of the existing KOIs could in principle be
trojans themselves, with a primary planet orbiting outside of the transiting
plane. A few examples are given for which this is a readily testable scenario.
