Google's latest Chrome for iOS (released this week) includes support for Google's bandwidth optimization service: "Over the coming days, we are also rolling out an experimental data compression service to help you save bandwidth, load pages faster, and browse more securely on your iPhone and iPad. Finally, this update brings fullscreen browsing to your iPad and the ability to access your browsing history from the menu".
"The latest Chrome browsers for Android and iOS can reduce cellular data usage and speed up mobile web browsing by using proxy servers hosted at Google to optimize website content. In our internal testing, this feature has been shown to reduce data usage by 50% and speed up page load times on cellular networks! .. The connection from the mobile device to the proxy runs over SPDY, an optimized protocol for the Web that is supported by Chrome, Firefox and Opera, and is also the basis for the forthcoming HTTP/2.0 standard being developed in the IETF .. secure connections (HTTPS) are routed directly from your mobile device to the destination, bypassing the optimization proxy – only HTTP requests are routed through and optimized by the proxy".
See "Better integration between Chrome and Google apps" - here.