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Share-based Compensation (Tables)
3 Months Ended
Mar. 31, 2021
Share-based Payment Arrangement [Abstract]  
Summary of Stock-Based Compensation A summary of our aggregate share-based compensation expense is set forth below: 
 Three months ended
March 31,
 20212020
 in millions
Liberty Global:
Performance-based incentive awards (a)$24.0 $27.7 
Non-performance based incentive awards25.4 18.3 
Other (b)7.4 6.2 
Total Liberty Global 56.8 52.2 
Other6.6 3.0 
Total
$63.4 $55.2 
Included in:
Other operating expense$1.2 $0.7 
SG&A expense62.2 54.5 
Total
$63.4 $55.2 
_______________

(a)Includes share-based compensation expense related to performance-based restricted share units (PSUs).

(b)Represents annual incentive compensation and defined contribution plan liabilities that have been or are expected to be settled with Liberty Global ordinary shares. In the case of the annual incentive compensation, shares have been or will be issued to senior management and key employees pursuant to a shareholding incentive program. The shareholding incentive program allows these employees to elect to receive up to 100% of their annual incentive compensation in ordinary shares of Liberty Global in lieu of cash.
Schedule of Stock Option Activity
The following table provides the aggregate number of options, share appreciation rights (SARs) and performance-based share appreciation rights (PSARs) with respect to awards issued by Liberty Global that were (i) outstanding and (ii) exercisable as of March 31, 2021:
Class AClass C
Gross number of shares underlying option, SAR and PSAR awards (a)Weighted Average exercise or base priceGross number of shares underlying option, SAR and PSAR awards (a)Weighted Average exercise or base price
Held by Liberty Global employees:
Outstanding23,236,280 $27.14 50,958,171 $26.02 
Exercisable12,093,245 $32.07 28,036,342 $30.22 
Held by former Liberty Global employees (b):
Outstanding1,413,040 $34.11 3,140,085 $32.23 
Exercisable1,396,581 $34.09 3,107,117 $32.21 
_______________
(a)Amounts represent the gross number of shares associated with option, SAR and PSAR awards issued to our current and former employees and our directors. Our company settles SARs and PSARs on a net basis when exercised by the award holder, whereby the number of shares issued represents the excess value of the award based on the market price of the respective Liberty Global shares at the time of exercise relative to the award’s exercise price. In addition, the number of shares issued is further reduced by the amount of the employee’s required income tax withholding.

(b)Amounts represent certain share-based awards that continue to be held by former employees of Liberty Global subsequent to certain split-off or disposal transactions. Although future exercises of these awards by former employees will not result in the recognition of share-based compensation expense, such exercises will increase the number of our outstanding ordinary shares.
Schedule of Other Share Based Compensation Activity
The following table provides the aggregate number of restricted share units (RSUs) and PSUs that were outstanding as of March 31, 2021. The number of shares to be issued on the vesting date of these awards will be reduced by the amount of the employee’s required income tax withholding.
Class AClass BClass C
Held by Liberty Global employees:
RSUs2,325,394 — 4,653,691 
PSUs1,761,952 660,000 3,523,923