Yalp Store lets you download apps from Google Play Store as apk files. It can search for updates of installed apps and lets you search for other apps. Yalp saves downloaded apks to your default download folder. Other features include browsing categories, viewing and leaving reviews, black/white-listing apps for updates, filtering apps by being free/paid and containing/not containing ads.
To supplement the features related to Google Play, Yalp Store has ordinary package manager features: listing, running, installing and uninstalling local apps.
If root is available, Yalp Store can update your apps in background, install and uninstall system apps.
By default Yalp Store connects to Google services using a built-in account, so you do not have to own a Google account to use it. The only reason to use a live Google account is to access the paid apps you own.