This is how I defined the share activity in the Manifest file.
<activity android:windowSoftInputMode="stateHidden" android:launchMode="singleTop" android:name="share" android:label="Browser app" android:screenOrientation="portrait" android:theme="@android:style/Theme.Black.NoTitleBar">
<intent-filter>
<action android:name="android.intent.action.SEND" />
<category android:name="android.intent.category.DEFAULT" />
<data android:mimeType="text/plain"/>
</intent-filter>
</activity>
And the share part actually works. I can get the url shared by browser, using activity.GetStartingIntent and intent.GetExtra, inside the Activity_Create.
It is just that I cannot get the chooser window for any kind of intent. And no, it doesn't start any other activity. It has an activity.finish given at the end of Activity_Create, but even when I commented that line, the chooser window doesn't show up.