Large earthquakes trigger very small earthquakes globally during passage of the seismic waves and during the following several hours to days1, 2, 3, 4, 5, 6, 7, 8, 9, 10, but so far remote aftershocks of moment magnitude M≥5.5 have not been identified11, with the lone exception of an M=6.9 quake remotely triggered by the surface waves from an M=6.6 quake 4,800 kilometres away12. The 2012 east Indian Ocean earthquake that had a moment magnitude of 8.6 is the largest strike-slip event ever recorded. Here we show that the rate of occurrence of remote M≥5.5 earthquakes (>1,500 kilometres from the epicentre) increased nearly fivefold for six days after the 2012 event, and extended in magnitude to M≥7. These global aftershocks were located along the four lobes of Love-wave radiation; all struck where the dynamic shear strain is calculated to exceed 10-7 for at least 100 seconds during dynamic-wave passage. The other M≥8.5 mainshocks during the past decade are thrusts; after these events, the global rate of occurrence of remote M≥5.5 events increased by about one-third the rate following the 2012 shock and lasted for only two days, a weaker but possibly real increase. We suggest that the unprecedented delayed triggering power of the 2012 earthquake may have arisen because of its strike-slip source geometry or because the event struck at a time of an unusually low global earthquake rate, perhaps increasing the number of nucleation sites that were very close to failure.