Why do PE firms dilute their stock so much?

PE firms like Blackstone, KKR, and Apollo have seen their number of shares outstanding skyrocket over time. Is this because whenever they need to capitalize a project, they issue new stock, than expect the cash they raise to perform better in the private market than their stock in the public market? If this is the case, why did they repurchase $1.9b worth of stock last quarter? Is it because they issue an outsize amount of stock to employees? Very confused, because their total comp was $686 million.