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This is a joint work with Piotr Przytycki from Wroclaw. Systolic (or simplicially non-positively curved) complexes are simplicial complexes whose properties resemble the ones of non-positively curved spaces. We define and study an ideal boundary of a systolic complex admitting a geometric action of a group (systolic group). For a free action our boundary is an example of the EZ-structure defined by Bestvina and Farrel-Lafont. In this case, the existence of such a structure implies e.g. that the Novikov conjecture holds for the group acting on the complex.