I made a workaround, the idea is that you create a function field(store=True) of type char that copy the date string detail to the function field, the level of detail is determined by that you want to group, if you want to group by day copy the datetime till the day.

Then you add that new field in your groupby filters in the searchview you want

This is an old question, but I thought I would add some code in case anyone is trying to do this. Mine was adding a sort by day field to account_voucher, so you may need to adjust yours to whatever you are trying to inherit. I am not putting the whole code, just the relevant snippets.

your_module.py

class ec_account_voucher(osv.osv):
    _inherit = 'account.voucher'
    _name = 'account.voucher'
    def _get_string_date(self, cr, uid, ids, name, args, context=None):
        res = {}
        for voucher in self.browse(cr, uid, ids, context=context):
            res[voucher.id] = str(voucher.date)
        return res
    _columns = {
    'x_string_date': fields.function(_get_string_date, type='char', string='Date (String)', store=True)
    }

your_module_view.xml

       <record model="ir.ui.view" id="voucher_form_ec">
          <field name="name">account.voucher.tree.inherit</field>
          <field name="model">account.voucher</field>
          <field name="inherit_id" ref="account_voucher.view_voucher_tree"/>
          <field name="arch" type="xml">
             <field name="date" position="after">
                <field name="x_string_date" invisible="1"/>
             </field>
          </field>
       </record>
        <record id="ec_view_voucher_filter" model="ir.ui.view">
            <field name="name">account.voucher.select.inherit</field>
            <field name="model">account.voucher</field>
            <field name="inherit_id" ref="account_voucher.view_voucher_filter_vendor_pay"/>
            <field name="arch" type="xml">
               <xpath expr="//filter[@string='Status']" position="before">
                  <filter string="Day" icon="terp-go-month" domain="[]" context="{'group_by':'x_string_date'}"/>
               </xpath>
            </field>
        </record>

Hope that helps someone!