public class FilesManager : IFilesManager
{
    private const int CREATE_FILE_REQUEST_CODE = 123;
    private static Context _context;

    public static void Init(Context context)
    {
        _context = context;
    }

    public async Task SaveFile(string fileName, byte[] content)
    {
        Intent intent = new Intent(Intent.ActionCreateDocument);
        intent.AddCategory(Intent.CategoryOpenable);
        intent.SetType(your_file_mimeType);
        intent.PutExtra(Intent.ExtraTitle, fileName);

        var activity = (MainActivity)_context;
        var listener = new ActivityResultListener(activity);
        activity.StartActivityForResult(intent, CREATE_FILE_REQUEST_CODE);

        var result = await listener.Task;

        if (result == null)
        {
            // Cancelled by user
            return;
        }

        using (Stream os = _context.ContentResolver.OpenOutputStream(result.Data))
        {
            os?.Write(content);
            os?.Close();
        }
    }

    private class ActivityResultListener
    {
        private readonly TaskCompletionSource<Intent> Complete = new TaskCompletionSource<Intent>();
        public Task<Intent> Task { get { return this.Complete.Task; } }

        public ActivityResultListener(MainActivity activity)
        {
            // subscribe to activity results
            activity.ActivityResult += OnActivityResult;
        }

        private void OnActivityResult(int requestCode, Result resultCode, Intent data)
        {
            if(requestCode != CREATE_FILE_REQUEST_CODE)
            {
                return;
            }

            // unsubscribe from activity results
            var activity = (MainActivity)_context;
            activity.ActivityResult -= OnActivityResult;

            // process result
            if (resultCode == Result.Ok)
            {
                Complete.TrySetResult(data);
            }
            else
            {
                Complete.TrySetResult(null);
            }
        }
    }