The N55 engine uses 2 deflection rollers in the serpentine belt system. This pulley is the larger of the 2, measuring 90mm (3.54") in diameter.
This part is listed by BMW as BMW part number 11287578675 and is described as INA OEM Deflection Pulley (90mm) - 11287578675 - E82,E90,E92,E93.
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BMW Fitments:
1 Series
E82 / E88 (08-13) > 135i N55 (11-13)
E82 / E88 (08-13) > 135is N55 (11-13)
3 Series
E90 / E91 / E92 / E93 (06-13) > 335i N55 (11-13)
E90 / E91 / E92 / E93 (06-13) > 335xi N55 (11-13)
X1 Series
E84 X1 (2013-2015) > X1 35i xDrive