diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index c74134708e1..9bcdda87e56 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -24,7 +24,7 @@ New Features
 ~~~~~~~~~~~~
 - Added new method :py:meth:`DataArray.to_dask_dataframe`, convert a dataarray into a dask dataframe (:issue:`7409`).
   By `Deeksha <https://github.com/dsgreen2>`_.
-- Add support for lshift and rshift binary operators (`<<`, `>>`) on
+- Add support for lshift and rshift binary operators (``<<``, ``>>``) on
   :py:class:`xr.DataArray` of type :py:class:`int` (:issue:`7727` , :pull:`7741`).
   By `Alan Brammer <https://github.com/abrammer>`_.
 
@@ -39,7 +39,8 @@ Deprecations
 
 Bug fixes
 ~~~~~~~~~
-
+- Fix groupby binary ops when grouped array is subset relative to other. (:issue:`7797`).
+  By `Deepak Cherian <https://github.com/dcherian>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index a6d63b7e95f..06788505161 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -669,7 +669,9 @@ def _binary_op(self, other, f, reflexive=False):
             obj = obj.where(~mask, drop=True)
             codes = codes.where(~mask, drop=True).astype(int)
 
-        other, _ = align(other, coord, join="outer")
+        # codes are defined for coord, so we align `other` with `coord`
+        # before indexing
+        other, _ = align(other, coord, join="right")
         expanded = other.isel({name: codes})
 
         result = g(obj, expanded)
diff --git a/xarray/tests/test_groupby.py b/xarray/tests/test_groupby.py
index 48a9c17d2a8..4258f6fe6d5 100644
--- a/xarray/tests/test_groupby.py
+++ b/xarray/tests/test_groupby.py
@@ -829,11 +829,33 @@ def test_groupby_math_bitshift() -> None:
         }
     )
 
+    left_manual = []
+    for lev, group in ds.groupby("level"):
+        shifter = shift.sel(level=lev)
+        left_manual.append(group << shifter)
+    left_actual = xr.concat(left_manual, dim="index").reset_coords(names="level")
+    assert_equal(left_expected, left_actual)
+
     left_actual = (ds.groupby("level") << shift).reset_coords(names="level")
     assert_equal(left_expected, left_actual)
 
+    right_expected = Dataset(
+        {
+            "x": ("index", [0, 0, 2, 2]),
+            "y": ("index", [-1, -1, -2, -2]),
+            "level": ("index", [0, 0, 4, 4]),
+            "index": [0, 1, 2, 3],
+        }
+    )
+    right_manual = []
+    for lev, group in left_expected.groupby("level"):
+        shifter = shift.sel(level=lev)
+        right_manual.append(group >> shifter)
+    right_actual = xr.concat(right_manual, dim="index").reset_coords(names="level")
+    assert_equal(right_expected, right_actual)
+
     right_actual = (left_expected.groupby("level") >> shift).reset_coords(names="level")
-    assert_equal(ds, right_actual)
+    assert_equal(right_expected, right_actual)
 
 
 @pytest.mark.parametrize("use_flox", [True, False])
@@ -1302,8 +1324,15 @@ def test_groupby_math_not_aligned(self):
         expected = DataArray([10, 11, np.nan, np.nan], array.coords)
         assert_identical(expected, actual)
 
+        # regression test for #7797
+        other = array.groupby("b").sum()
+        actual = array.sel(x=[0, 1]).groupby("b") - other
+        expected = DataArray([-1, 0], {"b": ("x", [0, 0]), "x": [0, 1]}, dims="x")
+        assert_identical(expected, actual)
+
         other = DataArray([10], coords={"c": 123, "b": [0]}, dims="b")
         actual = array.groupby("b") + other
+        expected = DataArray([10, 11, np.nan, np.nan], array.coords)
         expected.coords["c"] = (["x"], [123] * 2 + [np.nan] * 2)
         assert_identical(expected, actual)
 
@@ -2289,3 +2318,20 @@ def test_resample_cumsum(method: str, expected_array: list[float]) -> None:
     actual = getattr(ds.foo.resample(time="3M"), method)(dim="time")
     expected.coords["time"] = ds.time
     assert_identical(expected.drop_vars(["time"]).foo, actual)
+
+
+def test_groupby_binary_op_regression() -> None:
+    # regression test for #7797
+    # monthly timeseries that should return "zero anomalies" everywhere
+    time = xr.date_range("2023-01-01", "2023-12-31", freq="MS")
+    data = np.linspace(-1, 1, 12)
+    x = xr.DataArray(data, coords={"time": time})
+    clim = xr.DataArray(data, coords={"month": np.arange(1, 13, 1)})
+
+    # seems to give the correct result if we use the full x, but not with a slice
+    x_slice = x.sel(time=["2023-04-01"])
+
+    # two typical ways of computing anomalies
+    anom_gb = x_slice.groupby("time.month") - clim
+
+    assert_identical(xr.zeros_like(anom_gb), anom_gb)