Income taxes - Changes in unrecognized tax benefits (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Changes in unrecognized tax benefits
Balance, beginning of the year	$ 132	$ 133	$ 119
Gross increases related to current period tax positions	9	5	7
Gross increases related to prior period tax positions	13	6	10
Decrease related to resolution of audits with tax authorities	(28)
Expiration of the statute of limitations	(22)	(21)	(6)
Foreign currency translation	(10)
Foreign currency translation		9	3
Balance, end of year	$ 94	$ 132	$ 133

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

No definition available.

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- Definition

Amount of unrecognized tax benefits.

+ References

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Amount of decrease in unrecognized tax benefits resulting from foreign currency translation.

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Amount of decrease in unrecognized tax benefits resulting from settlements with taxing authorities.

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Amount of increase in unrecognized tax benefits resulting from tax positions that have been or will be taken in current period tax return.

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Amount of increase in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

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Amount of decrease in unrecognized tax benefits resulting from lapses of applicable statutes of limitations.

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