diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index 6ab42dda865e7..6cad9cdd6528f 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -397,7 +397,7 @@ def _insert_on_column(self, result: "DataFrame", obj: "DataFrame"):
 
         if self.on is not None and not self._on.equals(obj.index):
             name = self._on.name
-            extra_col = Series(self._on, index=obj.index, name=name)
+            extra_col = Series(self._on, index=self.obj.index, name=name)
             if name in result.columns:
                 # TODO: sure we want to overwrite results?
                 result[name] = extra_col
@@ -2268,7 +2268,7 @@ def _get_window_indexer(self, window: int) -> GroupbyRollingIndexer:
         """
         rolling_indexer: Type[BaseIndexer]
         indexer_kwargs: Optional[Dict] = None
-        index_array = self.obj.index.asi8
+        index_array = self._on.asi8
         if isinstance(self.window, BaseIndexer):
             rolling_indexer = type(self.window)
             indexer_kwargs = self.window.__dict__
diff --git a/pandas/tests/window/test_grouper.py b/pandas/tests/window/test_grouper.py
index 0eebd657e97b7..b93f9d5076b61 100644
--- a/pandas/tests/window/test_grouper.py
+++ b/pandas/tests/window/test_grouper.py
@@ -416,3 +416,32 @@ def test_groupby_rolling_empty_frame(self):
         result = expected.groupby(["s1", "s2"]).rolling(window=1).sum()
         expected.index = pd.MultiIndex.from_tuples([], names=["s1", "s2", None])
         tm.assert_frame_equal(result, expected)
+
+    def test_groupby_rolling_string_index(self):
+        # GH: 36727
+        df = pd.DataFrame(
+            [
+                ["A", "group_1", pd.Timestamp(2019, 1, 1, 9)],
+                ["B", "group_1", pd.Timestamp(2019, 1, 2, 9)],
+                ["Z", "group_2", pd.Timestamp(2019, 1, 3, 9)],
+                ["H", "group_1", pd.Timestamp(2019, 1, 6, 9)],
+                ["E", "group_2", pd.Timestamp(2019, 1, 20, 9)],
+            ],
+            columns=["index", "group", "eventTime"],
+        ).set_index("index")
+
+        groups = df.groupby("group")
+        df["count_to_date"] = groups.cumcount()
+        rolling_groups = groups.rolling("10d", on="eventTime")
+        result = rolling_groups.apply(lambda df: df.shape[0])
+        expected = pd.DataFrame(
+            [
+                ["A", "group_1", pd.Timestamp(2019, 1, 1, 9), 1.0],
+                ["B", "group_1", pd.Timestamp(2019, 1, 2, 9), 2.0],
+                ["H", "group_1", pd.Timestamp(2019, 1, 6, 9), 3.0],
+                ["Z", "group_2", pd.Timestamp(2019, 1, 3, 9), 1.0],
+                ["E", "group_2", pd.Timestamp(2019, 1, 20, 9), 1.0],
+            ],
+            columns=["index", "group", "eventTime", "count_to_date"],
+        ).set_index(["group", "index"])
+        tm.assert_frame_equal(result, expected)