Large earthquakes trigger very small earthquakes globally during passage of the seismic waves and during the following several hours to days^{1, 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.