No cualquier APK funciona. Debes buscar un sitio confiable como APKMirror (propiedad de la misma fundación que Android Police). Sigue estos pasos:
Descargar Google Play Store APK para Android 4.2.2 Update: Guía Completa descargar google play store apk para android 4.2.2 update
Users may seek this update for several reasons: No cualquier APK funciona
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Ultimately, the effort to update the Google Play Store on Android 4.2.2 highlights the resilience of the Android ecosystem but also its fragmentation. While it is technically possible to extend the life of a 2012 device through manual APK updates, the experience is increasingly diminishing. Google and app developers are dropping support for older APIs, meaning that even with a successfully updated Play Store, the catalog of compatible apps is shrinking rapidly.